Closest approach of a quantum projectile

TL;DR

This paper investigates quantum Rutherford scattering during head-on collisions, revealing that quantum effects prevent the projectile from approaching as closely as in classical physics, with the closest approach influenced by the wave function's spread.

Contribution

It demonstrates how quantum mechanics alters the closest approach in Coulomb scattering, highlighting the role of wave function spread and Ehrenfest's theorem discrepancies.

Findings

Quantum projectile cannot approach as closely as classical prediction.

Closest approach depends on the wave function's position spread.

Discrepancy between Ehrenfest's and Hamilton's dynamics in this context.

Abstract

We consider the simplest case of Rutherford scattering, i.e. the head-on collision, where the projectile is treated quantum mechanically. The convexity of repulsive Coulomb force invokes a disagreement between the Ehrenfest's and Hamilton's dynamics. We show that the quantum projectile cannot approach as close as the corresponding classical one, and that the average distance of closest approach depends on the position spread of the wave function describing the projectile.