Dynamical generation of electron motions in ground state H2+, in ground state H2 and in the first excited state of H2

Abstract

Using the recent formulation of Gell-Mann and Hartle for approximating quantum dynamical phenomena by means of classical equations, we simulate electron motions in ground state H2+, in ground state H2, and in the first excited state of H2. The approach develops approximate initial data first by mathematical bisection. The dynamical calculations are then carried out over short time intervals only, which is consistent with the Gell-Mann and Hartle theory and which is applicable because the phenomena to be studied are periodic. An energy conserving numerical scheme is used so that the energy of a given system will be a numerical invariant. Graphical representation of the electron motions indicate readily electron distributions, or clouds, over various time intervals.