Quantum Dynamics in a Time-dependent Hard-Wall Spherical Trap

TL;DR

This paper provides an exact quantum solution for a particle in a spherical trap with moving walls, analyzing dynamics during expansion and contraction, and comparing with simpler models.

Contribution

It introduces an exact solution for the Schrödinger equation in a time-dependent spherical boundary, extending previous models to spherical geometries.

Findings

Exact propagator for a particle in a moving spherical boundary

Comparison with infinite square well propagator

Numerical results for contracting and expanding spheres

Abstract

Exact solution of the Schr\"{o}dinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is constructed and compared with the propagator of a particle in an infinite square well with one wall in uniform motion.