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DOI: 10.1039/D5RP00030K (Review Article) Chem. Educ. Res. Pract., 2025, Advance Article

A review of research on the teaching and learning of quantum mechanics

Slade C. McAfee, Field M. Watts and Jon-Marc G. Rodriguez*
Department of Chemistry and Biochemistry, University of Wisconsin – Milwaukee, Milwaukee, Wisconsin 53211, USA. E-mail: rodrigjg@uwm.edu

Received 20th January 2025 , Accepted 25th April 2025

First published on 25th April 2025

Abstract

In this work, we review research on the teaching and learning of quantum mechanics in chemistry courses. This systematic review builds on previous reviews in chemistry education research that focused on the other highly quantitative, calculation-heavy topics covered in upper-level physical chemistry courses (kinetics and thermodynamics). We aim to provide a resource for both practitioners and education researchers. Based on the topics of the research conducted in our sample (N = 50), we grouped the articles into six categories: (1) students’ general challenges with quantum mechanics; (2) students’ conceptions of the atom; (3) students’ conceptions of bonding; (4) students’ conceptions of the quantum nature of light; (5) students’ conceptions of commonly used quantum mechanical models; (6) curricular materials and instruction. Relevant trends stemming from this work include that much of the research leans on education research in mathematics and physics to support the claim that students have difficulties with mathematics; however, these claims require further investigation within chemistry education contexts. Moreover, a suprising amount of research on quantum mechanics involved students sampled outside of upper-level chemistry courses (i.e., secondary-level and general chemistry contexts).

Introduction

Focusing on three fundamental topics – thermodynamics, kinetics, and quantum mechanics – the physical chemistry course sequence in the undergraduate chemistry curriculum is notoriously challenging for students (Holme, 2023). Many studies have been conducted related to the teaching and learning of thermodynamics (Bain et al., 2014) and kinetics (Bain and Towns, 2016) and have been synthesized to provide a resource for instructors and researchers. In the review on thermodynamics, Bain et al. (2014) used the extant literature to compile lists of students’ challenges related to the laws of thermodynamics, along with discussing the relationship between mathematics and physical chemistry. Although mathematical proficiency was found to correlate with a student's success in physical chemistry, Bain et al. (2014) found few studies that examined students’ understandings of mathematics topics related to thermodynamics. To this end, they posed the need for further interdisciplinary research and collaborations across chemistry and mathematics education to deepen our understanding of how to improve students’ learning of thermodynamics. In Bain and Towns (2016), when reviewing research related to the teaching and learning of chemical kinetics, they found these studies largely focused on secondary-level contexts. Similarly to the thermodynamics review, they echo the call for more interdisciplinary research, specifically between chemistry and mathematics, focusing on students’ reasoning of related rates and graphical representations (Bain and Towns, 2016). The remaining topic in physical chemistry, quantum mechanics, has yet to be reviewed within the context of the teaching and learning of chemistry.

Outside the context of chemistry, quantum mechanics is a content area that has been widely studied in physics education research. For example, reviews in physics education research reported trends such as students having challenges with quantum mechanics concepts such as wave-particle duality, wave functions, the uncertainty principle, and quantum tunnelling (Singh and Marshman, 2015; Krijtenburg-Lewerissa et al., 2017). Moreover, students often conflated ideas about classical and quantum mechanics (Singh and Marshman, 2015; Krijtenburg-Lewerissa et al., 2017). In one of the reviews, which focused specifically on secondary and early-tertiary education, students’ difficulties with atomic structure and models were discussed (Krijtenburg-Lewerissa et al., 2017). For example, students in a physics context were found to struggle with using models beyond the Bohr model, often resulting in the development of hybrid models of atomic structure (Ke et al., 2005). In a review focusing on upper-level physics students’ learning of quantum mechanics, students were found to be proficient with algorithmic questions while struggling with conceptual reasoning (Singh and Marshman, 2015). Additionally, Singh and Marshman (2015) highlighted that the difficulty associated with learning quantum mechanics is largely due to quantum mechanic's abstract nature and the level of mathematical sophistication required for a robust understanding. Although these quantum mechanics concepts are complex and abstract, the idea of introducing quantum mechanics concepts earlier in the physics curriculum has been suggested (Zollman et al., 2002). This is similar to the approach taken in the undergraduate chemistry curriculum, in which students learn about quantum mechanics qualitatively when discussing atomic structure in general chemistry (Holme et al., 2015). Nevertheless, considering the relationship between quantum mechanics concepts and mathematics, the question has been posed in mathematics education asking whether one could separate the two, commenting that students seem to fluidly problem-solve using concepts from both disciplines (Serbin and Wawro, 2024). To this end, there are many articles that forefront students’ reasoning regarding mathematical concepts, such as eigenfunctions and probability, contextualized using quantum mechanics (Close et al., 2013; Passante et al., 2018; Wan et al., 2019).

Given its extensive investigation in physics education research, the interdisciplinary nature of quantum mechanics is evident, a sentiment that has been the subject of conversation over the years. For example, in a recent special issue of the Journal of Chemical Education (JCE), the ways in which physical chemistry has changed over the last century of the journal's publications were discussed, highlighting the dependence of physical chemistry on mathematics and physics (Holme, 2023). The introduction to the special issue even mentioned that in the first volume of JCE in 1923, there were ongoing conversations regarding whether physical chemistry should be taught by a chemist, physicist, or mathematician (Holme, 2023). Along with this, in a review on the state of physical chemistry courses (Tsaparlis, 2007), many factors associated with students’ success in physical chemistry were reported; among them were mathematical ability, performance in prior physics courses, and motivation. In addition, Tsaparlis's (2007) review presented on a few student difficulties that were reported in the literature at that time. However, the previous review was published nearly twenty years ago and focused broadly on physical chemistry. To provide a tool for instructors that builds on the holistic knowledge generated in chemistry education we sampled all published articles that discuss quantum mechanics, including the few that were discussed by Tsaparlis (2007). Chemistry education has changed dramatically in the two decades since the publication of this review, and an updated review is needed to provide a tool for instructors and researchers. To this end, to better support students in this complex and interdisciplinary subject, it is important to consider evidence-based claims related to the teaching and learning of quantum mechanics.

Purpose

The quantum mechanics concepts that students learn in chemistry, particularly within a physical chemistry course sequence, are often abstract (Tsaparlis, 2007). Nevertheless, these abstract concepts have been identified as threshold concepts – concepts that, once learned, present pathways for new ways of thinking that were previously inaccessible (Körhasan and Wang, 2016). One example of this is that a student must first understand intermolecular forces before they can fully understand physical properties of matter (Talanquer, 2015). The key big ideas students learn in their physical chemistry courses are outlined in the Anchoring Chemistry Concept Map (ACCM) released by the American Chemical Society (Holme et al., 2018). Many of the concepts in the ACCM involve principles from quantum mechanics that assist in modelling the structure of an atom and the phenomenon of chemical bonding. Moreover, these concepts contain jarring amounts of calculus in comparison to a student's prior chemistry coursework, and a detailed presentation of these mathematical foundations are important for students to obtain a deep understanding of chemistry concepts. Although students recognize the amount of math that is required in quantum mechanics, students’ problem-solving mindsets have been found to emphasize reaching answers over developing a deep conceptual understanding of quantum mechanics (Gardner and Bodner, 2007).

With this in mind, we aim to synthesize the chemistry education literature that investigates the teaching and learning of quantum mechanics, with our concluding remarks related to implications for practice framed around the pedagogical content knowledge framework to provide accessible implications for instructors (Rodriguez and Towns, 2019). We also provide suggestions regarding future research in this area. Our findings and the scope of our review are intended to mirror the previous reviews on thermodynamics (Bain et al., 2014) and kinetics (Bain and Towns, 2016) to contribute to the collective synthesis of research on the teaching and learning of central topics in physical chemistry.

Methods

Sampling

Our approach for identifying articles to include in this review followed the best practices and guidelines for reporting systematic reviews (Page et al., 2021), which entailed first articulating our inclusion criteria. Our sample included articles that dealt with the teaching and learning of quantum mechanics, situated within a chemistry context. Articles were required to be peer-reviewed, empirical research articles (i.e., including research questions or aims, methods, and findings, etc.) with a primary focus on quantum mechanics topics. Articles at both secondary and tertiary educational contexts were included. An overview of the data collection is provided in Fig. 1. In short, we first searched the Education Research Information Center (ERIC) database, Chemistry Education Research and Practice (CERP), and the Journal of Chemical Education (JCE) using the search terms “chemistry” and “quantum mechanics”, with our sample current up to January 13, 2025. Following the removal of duplicates, we scanned the title, abstract, and full text of the remaining articles to determine whether they met the inclusion criteria. Lastly, we iteratively reviewed the citations for additional potential articles and evaluated them based on our criteria. In total, our final sample was N = 50 articles.
image file: d5rp00030k-f1.tif
Fig. 1 A PRISMA flow diagram detailing the article selection process. The first box shows the search engines we initially used to source articles. The rest of the boxes alternate to show the journals from which these articles are sourced. The JCE (Journal of Chemical Education), CERP (Chemistry Education Research and Practice), and ERIC (Education Resources Information Center) search yielded additional articles from Other Journals, which included Education Sciences, International Journal of Science Education, Journal of Baltic Science Education, Journal of College Science Teaching, Journal of Research in Science Teaching, and Science Education International.

Data analysis

Through an iterative process of reading the included articles, we sorted the key findings into six broad categories that emerged from the data: (1) students’ general challenges with quantum mechanics; (2) students’ conceptions of the atom; (3) students’ conceptions of bonding; (4) students’ conceptions of the quantum nature of light; (5) students’ conceptions of commonly used quantum mechanical models; (6) curricular materials and instruction. The categories were not mutually exclusive, with some articles being in multiple categories (i.e., students’ interpretations of the particle-in-a-box quantum mechanical model and atomic structure). As part of the analysis process, we read the articles and took detailed notes and memos on key findings, methodological details (qualitative, mixed, quantitative), the underpinning theoretical frameworks, and other salient information about a study. In the case of delineating between study design types, we made the distinction based on the nature of the data collected and what type of data were used to support claims, similar to other reviews by the authors (Rodriguez et al., 2020, 2023). For example, our operationalization of quantitative emphasized the use of values (stemming from data sources such as selected-response instruments) to support claims, whereas qualitative involved studies that used text and words (stemming from sources such as interviews or open-ended surveys) to support claim, and when these qualitative data sources were quantitatively transformed to make claims about measures of central tendency or the spread of the data, we characterized the study as mixed. Alternatively, mixed could have involved collecting both qualitative and quantitative data sources. Regarding the theoretical frameworks, we used the review conducted by Rodriguez et al. (2023) as a foundation to determine whether a study discussed a framework. Two authors independently coded for methodology and presence of framework for each article and met to discuss disagreements until complete consensus was achieved.

Limitations

In our previous work that involved characterizing the norms of our field, we presented inductive categories related to types of self-reported limitations discussed in chemistry education research, such as study design, prompt/survey, sample, and bias (Rodriguez et al., 2024). Here, we use these categories as a tool to contextualize our findings. Aligning with study design, which focuses on limitations related to methodology, we reviewed and analyzed the literature only using qualitative analysis. We found qualitative methods to be appropriate for addressing our aim related to synthesizing research, consistent with the approaches used in the thermodynamics (Bain et al., 2014) and kinetics (Bain and Towns, 2016) reviews. Quantitative approaches are more common for other aims, such as when conducting a meta-analysis, where the goal is measuring the efficacy of interventions. Next, considering prompt/survey, which is related to how the scope is narrowed during data collection, we acknowledge the impact the search terms may have on our study. Replicating this review with a more extensive list of search terms may result in differences in findings; however, we addressed this concern by using terms that were broad enough to initially collect a large number of articles (i.e., if an article does not mention “quantum mechanics” it likely is beyond the scope of this review). Moreover, our inclusion criteria is relevant for defining and limiting the characteristics of our sample (i.e., articles), which reflected our interest in providing evidence-based claims. Finally, our review may be limited due to bias, in terms of our perspectives and assumptions as researchers. For example, though we described our functioning definition of “empirical research”, we acknowledge that this definition may be influenced by the experiences and expertise of the researchers. Additionally, bias may influence the coding we conducted on our sample that focused on the methodology and frameworks. To address this, regular discussions were had among our team related to less clear cases and consensus was required for code assignments.

Findings

In this section, we first provide a general overview of the characteristics of our sample to outline the current state of research on the teaching and learning of quantum mechanics. Following this, we discuss the use of theoretical frameworks in our sample and, finally, we discuss the major topical categories related to the research outcomes of these articles.

Overview of the sample

In terms of study design, across our sample (N = 50), we found that 48% (n = 24) of the articles were qualitative, 6% (n = 3) of the articles were quantitative, and 46% (n = 23) were mixed methods (Fig. 2). Although most of the articles in our review were conducted in the United States (40%, n = 20), a notable portion were conducted in Greece (28%, n = 14) (Fig. 3). Lastly, regarding the level of instruction, most articles involved students in general chemistry courses (30%, n = 17), with physical chemistry students being the focus of 28% (n = 16) of our included articles. Many of the articles investigated students’ reasoning related to quantum mechanics topics at the secondary level (19%, n = 11) (Fig. 4).
image file: d5rp00030k-f2.tif
Fig. 2 Overview of the methods used in the articles in our sample (N = 50).

image file: d5rp00030k-f3.tif
Fig. 3 A map indicating the number and location of articles (N = 50) included in our review.

image file: d5rp00030k-f4.tif
Fig. 4 Overview of the articles’ samples. The total number of articles in this bar graph is greater than the number of articles in our study because some articles had multiple datasets.

Framework use

In our sample, 60% (n = 30) of the articles used a theoretical framework to guide their research. Using the categorization presented by Rodriguez et al. (2023), most of these frameworks align with the assumptions of constructivism, such as knowledge-in-pieces (Balabanoff et al., 2020; Zarkadis et al., 2022), conceptual change (Shiland, 1997; Tsaparlis and Papaphotis, 2009), pedagogical content knowledge (Padilla and Van Driel, 2011; Mack and Towns, 2016), and analogical reasoning (Muniz and Oliver-Hoyo, 2014a; 2014b). Within constructivism, knowledge is assumed to be constructed by the learner and is influenced through factors like social interactions, accessibility, and language (Ferguson, 2007). Moreover, there was also a notable number of articles using the mental models framework (n = 6). Consistent with constructivism, this framework was derived from the conceptual change literature and focuses on the mental representations that individuals generate and rely on to explain and predict phenomena (Vosniadou and Brewer, 1992; Vosniadou, 1994). In some cases, the mental models framework was paired with additional frameworks to aid in data analysis and interpretation (e.g., knowledge-in-pieces or Johnstone's Triangle) (Zarkadis et al., 2017; Zarkadis and Papageorgiou, 2020). The mental models framework was typically used when investigating students’ understanding of atomic structure, with the findings from these articles primarily inductively noting the common types of non-normative models students constructed (e.g., atom-cell model, planetary model, hybrid model, etc.). Among the articles without a formal theoretical framework, operating within constructivist ideas, it was common for articles to emphasize cataloging students’ (unitary, stable) misconceptions related to quantum mechanics concepts. In the broader literature, it is not common to present misconceptions as a formal theoretical framework, with a misconceptions-based approach often reflecting more informal assumptions made by the researchers; nevertheless, in some cases it was explicitly identified by the authors as the guiding framework in a subset of articles in our sample (Tsaparlis and Papaphotis, 2002; Nakiboglu, 2003; Park and Light, 2009; Dangur et al., 2014). As a general note, disciplined-based education research is shifting away from an emphasis on misconceptions, citing concerns related to a deficit framing that limits insight regarding how to better scaffold students’ understanding (Elby, 2000; Maskiewicz and Lineback, 2013; Cooper and Stowe, 2018).

Based on the emphasis on highlighting potential challenges students have with the content, in the next few subsections, we discuss these challenges within the categories mentioned previously.

Students’ general challenges with quantum mechanics

The key findings related to students’ general challenges with quantum mechanics are presented below in Table 1. To begin, physical chemistry students were found to have generally negative dispositions toward quantum mechanics, finding the related mathematics to be rigorous and less connected to the observable world (Tsaparlis, 2016). Students were found to have difficulty distinguishing between quantum mechanical concepts that are intended to be understood as distinct from one another, such as distinguishing between shells and subshells (Taber, 2002b). Other articles showed that students tend to adopt vocabulary related to quantum mechanics without tying it to conceptual meanings (Taber, 2002a; Nakiboglu, 2003). This difficulty is highlighted through findings stating that a student's performance on algorithmic quantum mechanics questions is independent and non-indicative of a student's performance on conceptual questions (Tsaparlis, 1997; Ardac, 2002; Nakiboglu, 2003; Papaphotis and Tsaparlis, 2008a).
Table 1 Summary of key findings related to students’ general challenges with quantum mechanics (n = 7)
Articles Key findings
(Tsaparlis, 1997; Ardac, 2002; Nakiboglu, 2003; Papaphotis and Tsaparlis, 2008a) Students’ performance on algorithmic quantum mechanics questions is independent of their performance on conceptual quantum mechanics questions
(Taber, 2002a; Nakiboglu, 2003) Students tend to adopt vocabulary without conceptual meaning
(Taber, 2002b) Students tend to struggle with adequately distinguishing the differences between distinct quantum mechanical concepts
(Tsaparlis, 2016) Students have a negative disposition towards quantum chemistry
(Tsaparlis, 2016) Students find quantum mechanics difficult due to the mathematics, the “different logic”, and theoretical nature of quantum mechanics as they are less connected to the observable world
(Tsaparlis, 2016) Students found the math in quantum mechanics more difficult than the math in classical thermodynamics

Students’ conceptions of the atom

Many of the articles (n = 28) included in our review primarily focused on students’ conceptions of the atom. Considering the number of articles that fell in this category, we divide our discussion of the key findings into two sub-categories, atomic structure and the Bohr model.
Atomic structure. The key findings from the articles investigating atomic structure are summarized in Table 2. Articles that primarily focused on the teaching and learning of atomic structure found that students tend to have difficulties defining quantum orbital spin energies, the quantum numbers, and their relationship to magnetism (Zarkadis et al., 2021; Dorris and Rau, 2022). More generally, students also were found to have difficulty understanding the discrete and probabilistic nature of quantum mechanics, which are properties that distinguish quantum mechanics from many of the other topics that are covered throughout the chemistry curriculum (Tsaparlis and Papaphotis, 2009; Tsaparlis, 2016; Allred and Bretz, 2019; Roche Allred and Bretz, 2019). When it comes to quantum numbers, students have been found to have difficulties connecting them to their meaning (Sunyono et al., 2016; Zarkadis and Papageorgiou, 2020; Zarkadis et al., 2022), with the d orbitals being especially challenging (Sunyono et al., 2016). However, this challenge is compounded with the fact that students also have troubles distinguishing between shells, orbitals, and orbits (Nakiboglu, 2003; Stefani and Tsaparlis, 2009; Sunyono et al., 2016; Zarkadis and Papageorgiou, 2020). Most surprisingly, students also disagree about whether an atom can be physically observed (Derman et al., 2019).
Table 2 Summary of key findings related to students’ conceptions of atomic structure (n = 12)
Articles Key findings
(Zarkadis et al., 2021; Dorris and Rau, 2022) Students tend to have difficulty defining quantum orbital spin energy and its relationship to magnetism
(Tsaparlis and Papaphotis, 2002, 2009; Allred and Bretz, 2019; Roche Allred and Bretz, 2019) Students tend to have difficulty with the discrete and probabilistic nature of quantum mechanics
(Derman et al., 2019) Students tend to be unsure about whether an atom can be physically observed
(Nakiboglu, 2003; Stefani and Tsaparlis, 2009; Sunyono et al., 2016; Zarkadis and Papageorgiou, 2020) Students tend to conflate atomic shells, orbitals, and orbits
(Sunyono et al., 2016; Zarkadis et al., 2021, 2022) Students tend to have difficulty connecting quantum numbers to their meaning
(Sunyono et al., 2016) Students tend to struggle describing d orbitals and the quantum numbers that are related to them

The Bohr model. The articles’ key findings related to the Bohr model are summarized in Table 3. With many of our articles focusing on students’ conceptualizations of atomic structure, the Bohr model was often referenced by students, whether explicitly or implicitly. To begin, students were found to conflate classical and quantum ideas about orbitals, particle/wave duality, and quantum mechanical models including the Bohr model (Tsaparlis, 1997; Papaphotis and Tsaparlis, 2008b; Park and Light, 2009; Stefani and Tsaparlis, 2009; Allred and Bretz, 2019; Roche Allred and Bretz, 2019; Zarkadis et al., 2021; Dorris and Rau, 2022). The idea that students conflate classical and quantum ideas regarding the Bohr model is surprising considering that students tend to prefer to use the Bohr model when describing atomic structure unless specifically instructed to use a different model (Papageorgiou et al., 2016; Sunyono et al., 2016; Derman et al., 2019). Though the Bohr model is the model students rely on most often, students’ use of this model, along with other models for atomic structure, to explain and predict phenomena are often inconsistent and dependent upon context (Zarkadis et al., 2017). Most notably, the Bohr model was found to inhibit students’ construction of new knowledge about atomic structure and quantum chemistry more broadly (Nakiboglu, 2003; Papaphotis and Tsaparlis, 2008b; Park and Light, 2009; Stefani and Tsaparlis, 2009; Tsaparlis and Papaphotis, 2009; Zarkadis and Papageorgiou, 2020; Zarkadis et al., 2021, 2022).
Table 3 Summary of key findings related to students’ conceptions of the Bohr model (n = 16)
Articles Key findings
(Tsaparlis, 1997; Papaphotis and Tsaparlis, 2008b, 2; Park and Light, 2009; Stefani and Tsaparlis, 2009; Allred and Bretz, 2019; Roche Allred and Bretz, 2019; Zarkadis et al., 2021; Dorris and Rau, 2022) Students tend to conflate classical and quantum ideas about orbitals, quantum mechanical models (including the Bohr model), and particle/wave duality
(Papageorgiou et al., 2016; Sunyono et al., 2016; Derman et al., 2019) Students tend to prefer to use the Bohr model unless prompted otherwise
(Nakiboglu, 2003; Papaphotis and Tsaparlis, 2008b; Park and Light, 2009; Stefani and Tsaparlis, 2009; Tsaparlis and Papaphotis, 2009; Zarkadis and Papageorgiou, 2020; Zarkadis et al., 2021, 2022) The Bohr model tends to inhibit students’ construction of new knowledge about quantum chemistry
(Zarkadis et al., 2017) Students’ use of models for atomic structure were inconsistent and were context dependent including the Bohr model

Students’ conceptions of bonding

Many of the articles we included in this review investigated students’ conceptions of bonding, with articles that fell into this category focusing on students’ reasoning related to hybridization theory and/or molecular orbital theory. The main findings from these included articles are presented in Table 4.
Table 4 Summary of key findings related to students’ conceptions of bonding (n = 9)
Articles Key findings
(VandenPlas et al., 2021) Students tend to conflate the energy associated with making and breaking bonds
(Nimmermark et al., 2016) Students tend to use hybridization theory only when describing smaller organic molecules
(Salah and Dumon, 2014) Students tend to have unintegrated conceptions of molecular orbital theory and hybridization theory
(Wang and Barrow, 2013) Students tend to have difficulty connecting quantum mechanical models of bonding with experimentally determined molecular shapes and the polarity of molecules
(Tsaparlis and Papaphotis, 2009) Students tend to describe the linear combination of atomic orbitals to form molecular orbitals as a function of volume and not as a mathematical operation
(Taber, 2002a; Stefani and Tsaparlis, 2009) Students’ familiarity with valence bond structures tends to impede students from understanding delocalized bonds
(Taber, 2002b) Students tend to have difficulty using models of chemical systems that involve molecular orbitals
(Nakiboglu, 2003) Students tend to describe hybridization as the result of atoms following the octet rule

Relevant to bonding, one of the key findings we identified was that students tend to conflate the energy that is associated with the making and breaking of chemical bonds (VandenPlas et al., 2021). One of the possible reasons for this is that valence bond theory, and more broadly the octet rule, tends to act as a barrier for students’ learning about bonding, specifically related to students’ understanding of delocalized bonds (Taber, 2002a; Stefani and Tsaparlis, 2009). This becomes especially relevant when students try to connect quantum mechanical models of bonding (e.g., hybridization theory) to experimentally determined molecular shapes and a molecule's polarity (Wang and Barrow, 2013); often students described hybridization theory as a result from atoms following the octet rule (Nakiboglu, 2003). Students also have been found to only use hybridization theory when describing smaller organic molecules (Nimmermark et al., 2016). However, students also seem to have unintegrated conceptions of both hybridization theory and molecular orbital theory (Salah and Dumon, 2014), with students generally having difficulty using molecular orbitals to model chemical systems (Taber, 2002b). This may be, in part, due to the difficulties identified surrounding students’ conceptualization of linear combinations of atomic orbitals as a function of volume, instead of as mathematical operations (Tsaparlis and Papaphotis, 2009).

Students’ conceptions of the quantum nature of light

In this section, we summarize the findings related to each of the articles that discuss students’ conceptions of the quantum nature of light. The key findings from the n = 4 articles are presented below in Table 5.
Table 5 Summary of key findings related to students’ conceptions of the quantum nature of light (n = 4)
Articles Key findings
(Balabanoff et al., 2020) Students’ understandings differ based on how students use their prior knowledge and physical experience with light
(Balabanoff et al., 2020, 2022) Students tend to misapply the particle/wave understanding of light in different contexts
(Balabanoff et al., 2022) Students conflate classical mechanics with quantum mechanics
(Orgill and Crippen, 2010) Students avoid using energy diagrams to supplement their explanation of electron transitions
(Orgill and Crippen, 2010; Moon et al., 2018) Students tend to have difficulty connecting spectroscopic transitions with the appropriate electromagnetic radiation energy and molecular movement

Chemistry students learning about the quantum nature of light for the first time are often introduced to the photoelectric effect. One of the articles investigated students’ reasoning related to the photoelectric effect and identified three categories of student understanding (fragmented, developmental, and advanced) (Balabanoff et al., 2020). The students’ explanations of the photoelectric effect were rooted in their personal experience with light and often relied on an understanding of classical mechanics (Balabanoff et al., 2020, 2022). Chemistry students showed difficulty understanding the particle-wave duality of light and had difficulty explaining light waves (Balabanoff et al., 2022). Along with this, challenges were reported related to students’ understandings of light–matter interactions, which were subsequently addressed using writing-to-learn assignments (Moon et al., 2018). These assignments prompted students to revise their explanations of spectroscopic transitions, allowing students to correctly pair each spectroscopic transition with the appropriate electromagnetic radiation, and to discuss the molecular motion that corresponded to these transitions (Moon et al., 2018). However, students were found to have difficulty connecting spectroscopic transitions with their associated electromagnetic radiation energy and corresponding molecular movement (Orgill and Crippen, 2010; Moon et al., 2018). Additionally, when students were presented with energy diagrams and the Rydberg equation, students tended to rely on the equation to explain spectroscopic transitions rather than the energy diagram (Orgill and Crippen, 2010).

Students’ conceptions of commonly discussed quantum mechanical models

Here, we discuss our findings related to how students reason about common quantum mechanical models that are presented in a physical chemistry course (Table 6). Though there are only few of these articles, for clarity, we structure our discussion around the quantum mechanical model that is under focus from each of these articles.
Table 6 Summary of key findings related to students’ conceptions of commonly discussed quantum mechanical models (n = 4)
Articles Key findings
(Muniz et al., 2018) Students tend to prefer more complex models commenting that they are better suited, or more accurate than simple models
(Muniz et al., 2018; Beck et al., 2020) Students conflate models and model components with each other and with classical mechanics
(Muniz and Oliver-Hoyo, 2014b; Muniz et al., 2018) Students tend to have difficulty using the representations used in quantum mechanical models and their corresponding quantum numbers
(Muniz et al., 2018; Beck et al., 2020) Students avoid mathematization when applying quantum mechanical models
(Muniz and Oliver-Hoyo, 2014a) Students adopt language for describing quantum mechanical tunnelling without conceptual understanding

Particle-in-a-box. Four articles in the sample focused on students’ interpretations of the particle-in-a-box quantum mechanical model (Muniz and Oliver-Hoyo, 2014a, 2014b; Muniz et al., 2018; Beck et al., 2020). One of the key findings was students reporting the assumption that more complex models are more suited, or more accurate, than simpler models (Muniz et al., 2018). Students were also found to struggle with the representations that are used in this model (e.g., eigenfunctions) along with conceptualizing the meaning of quantum number n (Muniz and Oliver-Hoyo, 2014b). It was also observed that students conflate facets of the particle-in-a-box model with other models, which leads to misapplications of the model to real-world phenomena (Muniz et al., 2018; Beck et al., 2020). Along with this, students were found to adopt and use the language associated with this model without having a robust conceptual understanding of the content (Muniz and Oliver-Hoyo, 2014a).
Quantum mechanical harmonic oscillator. Two articles investigated students’ interpretations of another model, the quantum mechanical harmonic oscillator (Muniz et al., 2018; Beck et al., 2020). In the literature, students have shown difficulties with model application where they conflate facets of the model (Muniz et al., 2018; Beck et al., 2020). Along with this, students are found to avoid mathematizing models when possible (Muniz et al., 2018), and when they do, they focus primarily on surface features of quantum mechanical models, both lexical (e.g., the language used when describing the model) and complex (e.g., the intensity of the mathematics that is shown in the model) (Muniz et al., 2018). When describing the kinetic and potential energies of the harmonic oscillator, students used classical mechanics to build explanations (Beck et al., 2020).
Two-dimensional rigid rotor. There were a few articles that investigated students’ interpretations of the two-dimensional rigid rotor model (Muniz et al., 2018; Beck et al., 2020). In these articles, students were found to conflate vibrational and rotational motion when applying the model (Muniz et al., 2018; Beck et al., 2020). When using the two-dimensional rigid rotor system to predict and explain molecular rotation, students were found to focus on incorrect aspects of the model causing misapplication of the model (Beck et al., 2020).

Curricular materials and instruction

We found that many articles (n = 16) primarily focused on how quantum mechanics topics are taught, as opposed to students’ reasoning. To further elaborate on the key findings from these articles, we break the findings into two sub-categories, (1) curricular materials and (2) instruction.
Curricular materials. The key findings related to curricular materials are presented in Table 7 below. Several of the articles that focused on instructional materials used for teaching quantum mechanics involved analysing textbooks. In a study conducted by Tsaparlis (2014), they found that textbooks typically present quantum mechanics after their discussion of thermodynamics. In other work, textbooks that discuss quantum mechanics were found to not support students in their reasoning about quantum mechanics concepts such as quantum numbers or the use and limitations of historical quantum mechanical models of the atom (e.g., the plum pudding model) (Niaz and Fernández, 2008). Additionally, although textbooks may present historical quantum mechanical models of atomic structure, they often do not provide explanations for why quantum mechanics would need to exist in the first place (Shiland, 1997; Niaz and Fernández, 2008). Textbooks teaching about atomic structure were found to discuss the Bohr model without mentioning its limitations or the ways in which modern models rooted in quantum mechanics (e.g., orbitals) address these problems (Shiland, 1997). Even when textbooks presented orbitals, they often do not clarify the probabilistic nature of orbitals, supporting the tendency for students to view orbitals as physically observable objects (Niaz and Fernández, 2008). Along with this, textbooks often do not provide thorough discussions around the problems that quantum mechanics seeks to solve (e.g., explaining blackbody radiation or the photoelectric effect), nor do they facilitate students’ transitions in their reasoning from the laws of classical mechanics to the postulates of quantum mechanics (Shiland, 1997; Niaz and Fernández, 2008). Similarly to textbooks, Donnelly and Winkelmann (2021) found that syllabi for physical chemistry courses lack in their support of students’ learning by showing little relationship between course topics and their learning-centeredness.
Table 7 Summary of key findings related to curricular materials (n = 10)
Articles Key findings
(Donnelly and Winkelmann, 2021) Syllabi have little relationship between learning-centeredness and the topics focused on in the course
(Partanen, 2018, 2020) Active learning and other social factors play a central role in students’ learning of quantum mechanics and improve student learning
(Tsaparlis, 2014) Textbooks typically discuss quantum mechanics after they discuss thermodynamics
(Pérez García et al., 2016) The Quantum Chemistry Concept Inventory can measure students’ conceptual understandings of quantum mechanics
(Dangur et al., 2014; Dori et al., 2014) Textual and visual understandings of electronic structure, graphical reasoning, and general understandings of quantum mechanics can be supported through a visual-conceptual approach
(Niaz and Fernández, 2008) Textbooks do not support students in their thinking of quantum numbers for thinking about atomic structure
(Shiland, 1997; Niaz and Fernández, 2008) Textbooks do not provide a strong foundation for why quantum mechanics exists in the first place and do not facilitate the transition from teaching about classical mechanics to quantum mechanics
(Niaz and Fernández, 2008) Textbooks do not make a clear distinction between orbitals as mathematical outcomes and not physically observable objects
(Ruddick et al., 2012) A computational lab intervention helps students with the introduction of MO theory for small molecules
(Shiland, 1997) Textbooks do not present the shortcomings of the Bohr model or how quantum mechanics can correct for these shortcomings

Several of the other articles in this category focused on research-based pedagogical tools. For example, when investigating students’ textual and visual understandings of quantum mechanics representations and electron structure descriptions related to bonding and atomic structure, Dangur et al. (2014) and Dori et al. (2014) found that students could be better supported in developing these understandings using a visual-conceptual approach to teaching, which includes qualitative tools (e.g., graphical aids or models instead of the involved mathematics) that promote students’ visualization of quantum mechanics. Other alternative pedagogical strategies included using active learning to leverage social interactions to improve students’ understanding (Partanen, 2018, 2020). Along with these visual-conceptual approaches, computer laboratories were also found to support students when learning quantum chemical concepts related to molecular orbital theory and bonding (Ruddick et al., 2012). Outside the classroom context, the Quantum Chemistry Concept Inventory was developed which can be used in physical chemistry classrooms to measure students’ conceptual understandings of quantum chemical concepts.

Instructors. Key findings related to instructors teaching quantum mechanics concepts are presented in Table 8. Aside from research-based pedagogical strategies, another important part of classroom instruction on quantum mechanics are the instructors. Instructors were found to have well-informed ontological understandings of the atom which were informed by their interpretations of experimental evidence of quantum mechanics and its applications (Lemma and Belachew, 2022, 2023). It was also identified that instructors often focus on the findings that quantum mechanics can prove, which differs from undergraduate students’ perceptions of quantum mechanics which seem to largely focus on what quantum mechanics can disprove (Lemma and Belachew, 2023). In a nation-wide survey conducted in the United States, Fox and Roehrig (2015), found that instructors have beliefs about why quantum mechanics should be taught in the undergraduate chemistry curriculum, such as for building on students’ knowledge of fundamental chemical concepts and to assist students in their understanding of mathematical modelling in chemistry. These findings were expanded on in a phenomenographic study conducted by Mack and Towns (2016). Additionally, instructors believe that the social aspects of learning are a key component in building students’ conceptual understandings of abstract quantum mechanical concepts (Mack and Towns, 2016). Instructors seem focused on how well students are understanding concepts, the curriculum, and instructional strategies that assist students in constructing robust understandings of quantum mechanics; however, they consider assessments less often (Padilla and Van Driel, 2011). When it comes to curriculum, instructors reported teaching introductory quantum mechanical models (e.g., particle-in-a-box, quantum mechanical harmonic oscillator, two-dimensional rigid rotor, etc.) and the postulates of quantum mechanics and typically do not cover group theory or laser spectroscopy (Padilla and Van Driel, 2011; Fox and Roehrig, 2015).
Table 8 Summary of key findings related to instructors (n = 5)
Articles Key findings
(Lemma and Belachew, 2022, 2023) Instructors’ ontology of the atom appears to be well-informed by their interpretation of experimental evidence and applications of quantum mechanics
(Lemma and Belachew, 2023) Instructors tend to focus on what quantum mechanics has the power to prove, whereas undergraduates tend to focus on what quantum mechanics disproves
(Mack and Towns, 2016) Instructors believe quantum mechanics should be taught to build students’ knowledge of fundamental concepts
(Fox and Roehrig, 2015; Mack and Towns, 2016) Instructors believe the purpose of teaching quantum mechanics is to instruct students on the nature of mathematical modelling in the chemical sciences
(Mack and Towns, 2016) Instructors believe that social aspects of learning build students’ conceptual understandings of quantum mechanics
(Fox and Roehrig, 2015) Instructors do not typically cover symmetry and/or group theory and laser spectroscopy
(Padilla and Van Driel, 2011; Fox and Roehrig, 2015) Instructors typically teach the introductory models and the postulates of quantum mechanics
(Padilla and Van Driel, 2011) Instructors tend to focus on students’ understanding, curriculum, and instructional strategies employed and less on assessment approaches

Implications for practice

To enhance the accessibility and practicality for instructors interested in implementing these findings into their own courses, we frame our discussion using the pedagogical content knowledge (PCK) framework, which was originally proposed by Shulman (1986), but has since been expanded on by Hume et al. (2019), and we previously proposed its utility for framing implications stemming from research (Rodriguez and Towns, 2019). The PCK framework outlines five different areas of knowledge that instructors need to teach effectively, which extends beyond the instructor's understanding of the content knowledge.

Knowledge of students

The knowledge of students component of PCK outlines instructors’ understandings of the difficulties students face in relation to specific topics taught (Hume et al., 2019). With this review, we compiled lists of the reported challenges that students had related to quantum mechanics topics (Tables 1–7). With these lists, we provided a resource for instructors teaching quantum mechanics across education levels; however, our understanding of students’ knowledge is limited by most of the articles involving students who were not in upper-level physical chemistry courses. Many of the articles (30%, n = 17) recruited participants from first-year introductory chemistry courses. There were also a significant number of articles focusing on secondary students (22%, n = 11), which is primarily due to the large body of researched generated by Tsaparlis, Papaphotis, and Papageorgiou, who were investigating the efficacy of teaching quantum mechanics concepts in Greek high schools. Similar findings involving a large number of secondary students as study participants were presented in the review on the teaching and learning of kinetics (Bain and Towns, 2016). Although sampling from secondary contexts and general chemistry courses are a potentially productive and generative source of data, this body of research could benefit from conducting studies that involve students in upper-level courses. Further work focusing on physical chemistry students would be beneficial for understanding how to support their learning in a quantum mechanics course.

As for specific challenges reported that instructors should be aware of, one prominent theme throughout our review was the role that the Bohr model can play as a potential barrier for chemistry students. From these articles, we emphasize the importance of clarifying the limitations of the Bohr model to students, emphasizing that the intellectual need for modern quantum theory is rooted in how unsuccessful the Bohr model is at describing anything other than spectroscopic phenomena. Along with students’ tendency to fall back on the Bohr model when conceptualizing atomic structure, a similar and previously reported trend was identified related to the octet rule in relation to students’ conceptualizations of chemical bonding (Dood and Watts, 2022; Hunter et al., 2022).

Curricular knowledge

Curricular knowledge encompasses the knowledge that an instructor has about the curriculum broadly, including its context, its connections to other topics, and the purpose for teaching the content to students (Hume et al., 2019). There were a number of articles in our review that analysed textbooks that are used for teaching quantum mechanical concepts (Shiland, 1997; Niaz and Fernández, 2008; Tsaparlis, 2014). Tsaparlis (2014) reviewed the broad topical structure of physical chemistry textbooks and found that most textbooks discussed thermodynamics before quantum mechanics but presented pedagogical advantages to teaching quantum mechanics before thermodynamics (e.g., early exposure to quantum mechanics can be helpful as quantum mechanics is the foundation of contemporary physical chemistry research). Instructors should be prepared for the advantages and disadvantages for both approaches to better understand the difficulties that students may encounter depending on the order the topics are presented. With this analysis of physical chemistry textbooks, two other articles investigated textbook introductions of specific concepts, with both primarily pointing to textbooks’ limitations in supporting students in learning new quantum concepts, such as atomic modelling and quantum numbers (Shiland, 1997; Niaz and Fernández, 2008). As instructors, being aware of the limitations that have been identified in the literature regarding textbooks’ discussion of topics like atomic modelling is important for supporting students to build a robust understanding of quantum chemical concepts and enhance the transfer of these concepts to future topics discussed. However, there is a need for further work investigating curricular materials used in physical chemistry courses, as both textbook reviews presented here were conducted with high school and general chemistry textbooks.

Our review found that instructors in the Netherlands and in the United States typically teach foundational quantum mechanical models, as well as the postulates of quantum mechanics (Padilla and Van Driel, 2011; Fox and Roehrig, 2015). However, physical chemistry instructors in the United States often do not teach about group theory or laser spectroscopy (Fox and Roehrig, 2015). These similarities in curriculum across the United States may be due to the beliefs some physical chemistry instructors may have about the purposes for teaching quantum mechanics. Instructors were found to believe that it is important for chemistry students to learn quantum mechanics because it supports students’ understanding of fundamental concepts in chemistry as well as assists students in their skills with mathematical modelling in chemistry (Mack and Towns, 2016).

Pedagogical knowledge

The pedagogical knowledge component of PCK outlines instructors’ understanding of productive strategies for supporting students in their learning (Hume et al., 2019). In our sample, n = 13 of our articles were conducted using a pre-post, intervention design. These studies present different approaches that were effective, such as the use of analogies (Muniz and Oliver-Hoyo, 2014a), incorporation of visual elements during instruction (Dangur et al., 2014; Dori et al., 2014; Sunyono et al., 2016), and the use of writing-to-learn assignments to support students in reasoning about topics like light–matter interactions (Moon et al., 2018). We encourage interested instructors to incorporate these approaches into their instruction to support students with different topics in quantum mechanics. For researchers that intend to replicate these interventions or develop their own, we highlight the Quantum Chemistry Concept Inventory (Pérez García et al., 2016) to assess students’ understanding of quantum mechanics concepts, which was used by two articles in our sample (Partanen, 2018; Muniz et al., 2018).

To narrow the scope of our review, articles were removed based on not meeting sampling criteria, such as articles that were not formally empirical studies or articles involving work conducted outside of chemistry course contexts. Nevertheless, there were a number of articles in the broader literature base that propose strategies similar to those reported here (Budde et al., 2002; Vemulapalli and Byerly, 2004; Izquierdo-Aymerich and Adúriz-Bravo, 2009; Didiş, 2015; Barbee et al., 2018; Volfson et al., 2019). Some of these articles emphasized the importance of instruction on the history of philosophical interpretations of quantum chemical concepts (Justi and Gilbert, 2000; Niaz and Rodríguez, 2000; Scerri, 2000; Erduran, 2005; Garritz, 2013), providing useful resources for practitioners.

Content knowledge

The next component of PCK is content knowledge, which encompasses instructors’ understanding of the disciplinary content that is taught (Hume et al., 2019). An article included in our sample found that chemistry instructors from a university in Ethiopia had well-informed conceptualizations of the atom that is built on the empirical evidence of quantum mechanics (Lemma and Belachew, 2022). Instructors’ ontology of the atom differs from that of students, which may be due to their differences in interpretation of experimental findings: while instructors construct their understandings of quantum mechanical concepts by focusing on what quantum mechanics can prove, students may instead focus on the ideas that quantum mechanics can disprove (Lemma and Belachew, 2023). Further work could be conducted to investigate instructors’ conceptualizations of quantum mechanics concepts. However, there are other articles that were beyond the scope of this review that investigated pre-service teachers’ understandings of quantum mechanical concepts. These articles did not meet our inclusion criteria as the participants were not recruited from a chemistry context, but rather contexts like physics or education courses. However, in these articles, they were able to identify common challenges pre-service teachers may have, many of which were similar to the challenges reported in our review (Kiray, 2016; Temel and Özcan, 2018; Wiener, 2020).

Assessment knowledge

This component of PCK outlines instructors’ knowledge surrounding assessment (Hume et al., 2019). One article in our dataset found that instructors focus much less on assessment than on other components of PCK (Padilla and Van Driel, 2011), which is important because evaluating students’ understanding of abstract quantum mechanical concepts may require novel strategies that differ from traditional exams. This was the only article in our data set that investigated instructors’ understanding of assessment knowledge. More work is needed in this area to understand what support is necessary for instructors assessing students on quantum mechanics concepts. As an implication, through assessment instructors indicate what they value (Cooper, 2015); thus, part of improving assessment involves reflecting on the learning objectives and target outcomes for a course.

Implications for research

This review has synthesized a large body of extant literature that provides insight regarding students’ conceptualization of quantum mechanics. Although there was some overlap in identifying topics where students need more support – namely students’ understanding of particle-wave duality, conflating classical and quantum mechanics, and atomic modelling beyond the Bohr model – there were some differences in our review in comparison to the reviews conducted in a physics education context. Most notably, the physics reviews involve detailed discussions on students’ issues with specific mathematical operations that are necessary when learning quantum mechanics (Singh and Marshman, 2015; Krijtenburg-Lewerissa et al., 2017), whereas our sample in a chemistry context does not. The literature that was included in this study was found to rely heavily on the findings presented in physics and mathematics education research, especially when making claims about how students feel about the math that is utilized in quantum mechanics. Investigations on specific mathematical challenges that chemistry students face when learning these concepts are not as prevalent in our review, which may be due to the number of articles in our review that involved high school and general chemistry students where the mathematics emphasizes algebra or is abstracted completely to a qualitative description. Quantum mechanics is inherently interdisciplinary with related topics taught throughout the chemistry undergraduate curriculum. Future research in this area would be significantly strengthened through interdisciplinary work, bridging the gaps between chemistry, physics, and mathematics education research; as part of this, studies in chemistry that replicate or build on previous work conducted in physics and mathematics, such as investigating chemistry students’ perceptions and use of mathematics, would be an important contribution to our knowledge on the teaching and learning of quantum mechanics in chemistry education. Identifying ways to make these concepts more clearly connected for our shared students could create a pathway to learning these concepts that better supports students. Along with proposing the need for further interdisciplinary work, we also highlight the need for further work conducted outside of the United States and Greece, which were the context for most of the articles in our sample.

Additionally, we noted that physical chemistry instructors typically teach students about introductory quantum mechanical models (Padilla and Van Driel, 2011; Fox and Roehrig, 2015); however, our review only identified four articles that specifically investigated students’ understanding of these models. The articles that we included discussed the particle-in-a-box model, the quantum mechanical harmonic oscillator, and the two-dimensional rigid rotor. These three quantum mechanical models are not the only models that physical chemistry students learn. After instruction on the introductory models, students find the analytical solution to the hydrogen atom using the Schrödinger equation, discuss the challenges with quantum mechanics that arise with the three-body problem, and learn approximation methods that allow for exact solutions to the Schrödinger equation when modeling multi-electron atoms. Thus, there is a need for more research that investigates students’ interpretations of advanced models in physical chemistry, including interdisciplinary work between chemistry and mathematics education focusing on current understanding of students’ difficulties with this math-heavy modeling.

Lastly, we note, many of the studies in the sample did not have a formal theoretical framing, often focusing on identifying students’ misconceptions, suggesting a constructivist view which emphasizes misconceptions as students’ constructed knowledge that is stable and unitary (i.e., misconceptions constructivism) (Elby, 2000). In chemistry education research, there has been a recent increase in using an alternative model to describe students’ cognition, fine-grained constructivism, which emphasizes the context-dependence, emergent, and manifold nature of knowledge (e.g., resources framework and knowledge-in-pieces) (Rodriguez, 2024). Recent calls for moving beyond cataloguing misconceptions highlight the potential tendency to lean toward deficit-framing when identifying misconceptions because it emphasizes what students do not know without providing information regarding how to leverage what students do know, providing limited insight regarding ways to scaffold students’ learning (Cooper and Stowe, 2018). Although some of the articles in the sample used the mental models framework, as a community, it is worth reflecting on the assumptions of the frameworks we use and evaluate their application, such as its analytic and interpretive power (i.e., the extent the framework informs data collection and data analysis). For example, in the case of the mental models framework, its operationalization often did not directly inform data analysis. Moreover, we highlight the need for more work framed beyond constructivist frameworks, with our review mirroring the larger trend in chemistry education research, reflecting less work carried out within hermeneutic and critical theory frameworks (Rodriguez et al., 2023).

Concluding remarks

The instruction on quantum mechanics in chemistry is an exciting area of research with much more to learn. In this review, we synthesized research trends related to the following categories: students’ conceptions of the atom, students’ conceptions of bonding, students’ conceptions of the quantum nature of light, students’ conceptions of commonly used quantum mechanical models, and curricular materials and instruction. Throughout these findings, we noted the reliance of this body of literature on research outside the chemistry education research community related to students’ use of mathematics. Building on this, we highlight that much of this work was conducted in courses in which the quantum mechanics concepts were simplified for students (i.e., secondary education and general chemistry). To this end, we further emphasize the importance of interdisciplinary work and collaborations across chemistry, physics and mathematics to investigate students’ understanding of the mathematical foundations necessary for using advanced models in quantum mechanics and other topics in upper-level physical chemistry. Lastly, future work would benefit from utilizing diverse theoretical frameworks to further investigate students’ conceptualization of abstract quantum mechanics concepts and explore students’ experiences when learning quantum mechanics. That said, we echo the sentiment expressed previously by Hunter et al. (2022), “By reflecting on our theoretical assumptions, we can adopt new approaches to address modern challenges, advancing our field to improve the teaching and learning of chemistry” (p. 2461).

Author contributions

Slade C. McAfee investigation, writing – original draft, writing – review & editing, visualization; Field M. Watts conceptualization, methodology, investigation, writing – review & editing; Jon-Marc G. Rodriguez conceptualization, methodology, writing – review & editing, visualization, supervision.

Data availability

As described in the methods, the data can be obtained using commonly accessed databases or journal websites. All the articles in the sample are mentioned and cited in the findings and provided in the references list.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We would like to express our sincere appreciation for the support rendered by the YouTube channel Cozy Jazz Ambiance. Their calming energy and positive ambiance significantly contributed to our analytical and writing processes.

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