Spectral-moment constrained density matrices of maximum entropy for solvated electrons

Abstract

A single-particle density matrix for a solvated electron that pertains to its motion relative to its mean location has been obtained by maximizing its entropy subject to a constraint on the value of its Heisenberg Product. The latter quantity is the product of the mean dispersion-in-position and the mean dispersion-in-momentum of the solvated electron, which are determined by the inverse-first and first moments, respectively, of the solvated electron's optical absorption spectrum. The resulting density matrix is expressible as a canonical distribution function of a spherical-harmonic oscillator in equilibrium, with spectrally determined distribution modulus and force constant of the potential.