Trajectory of motion of an electron in the Coulomb scattering in terms of the Schroedinger wave equation and the Hamilton Jacobi equation

TL;DR

This paper compares quantum and classical electron trajectories in Coulomb scattering using Schrödinger and Hamilton-Jacobi equations, highlighting their correspondence and proposing optimal wave function dynamics for experimental verification.

Contribution

It introduces a method to derive electron trajectories from wave functions in Coulomb scattering and compares them with classical paths, offering insights into quantum-classical correspondence.

Findings

Good agreement between quantum and classical trajectories.

Identification of optimal wave function dynamics for experimental testing.

Comparison of spherical and Temple coordinate approaches.

Abstract

The trajectory of motion of a scattering electron in the Coulomb potential from the wave function of the Schroedinger equation is presented in two ways, spherical polar coordinates and Temple coordinates, and is compared with each other and with the corresponding motion of classical mechanics. A good correspondence among dynamics by wave functions and the classical dynamics has been acknowledged by comparing computed examples.Detailed computing examples discriminate the optimal dynamics of the wave function that should be verified by an experiment.