Linear Differential Equation for the Radial Distribution Function of Quantum Mechanics

15 March 1971

journal article
research article
Published by AIP Publishing in The Journal of Chemical Physics

Vol. 54 (6) , 2739-2741
https://doi.org/10.1063/1.1675238

Abstract

A nonlinear equation for the probability density of quantum theory is obtained from the Schrödinger equation for the case of complex wavefunctions. Motion of a particle in a centrally symmetric field is investigated and it is found that a linear differential equation for the radial distribution function can be derived. The linear equation is used to demonstrate the transition to classical theory and to derive a partial differential equation for the radial distribution function of statistical thermodynamics.

Keywords

PROBABILITY DENSITY
QUANTUM THEORY
LINEAR EQUATIONS
THERMODYNAMICS
FUNCTIONS
NONLINEAR EQUATION
RADIAL DISTRIBUTION FUNCTION
DIFFERENTIAL EQUATIONS
PROBABILITY
LINEAR DIFFERENTIAL EQUATION
QUANTUM MECHANICS
PARTIAL DIFFERENTIAL EQUATION

This publication has 1 reference indexed in Scilit:

A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
Physical Review B, 1952