A quantum particle in a box with moving walls

TL;DR

This paper studies the quantum behavior of a particle confined in a box with moving walls by transforming the problem into a fixed-box scenario with a time-dependent Schrödinger operator.

Contribution

It introduces a novel approach to analyze a quantum particle in a dynamic boundary condition by reformulating it into a fixed boundary problem with a time-dependent Hamiltonian.

Findings

Reformulation of moving wall problem into fixed box with time-dependent operator

Analysis of quantum dynamics with moving boundaries

Potential applications in quantum control and confinement

Abstract

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.