Quantum dynamics in a time-dependent cylindrical trap

TL;DR

This paper investigates the quantum dynamics of a particle in a cylindrical trap with a time-varying boundary, deriving analytical expressions and analyzing the effects of boundary changes on energy, momentum, and density profiles.

Contribution

It provides exact solutions for the Schrödinger equation in a time-dependent cylindrical geometry and discusses boundary change effects, including adiabatic and sudden limits.

Findings

Density profile exhibits diffraction-in-time pattern with enhanced fringes.

Analytical expressions for energy and momentum expectations are derived.

Numerical results show behavior during contracting and expanding boundaries.

Abstract

Solutions to the Schr\"{o}dinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the exact solutions; and the adiabatic and sudden change of the boundary are discussed. The density profile as a function of time in a given observation point, resembles the diffraction-in-time pattern observed in a suddenly released particle but with an enhanced fringe visibility. Numerical computations are presented for both contracting and expanding boxes.