Quantum particle displacement by a moving localized potential trap

TL;DR

This paper analyzes the quantum dynamics of a particle in a moving attractive delta potential, revealing probabilities of confinement, retention, and a novel double-speed movement, with exact solutions and a quasi-classical interpretation.

Contribution

It provides exact analytical results for a quantum particle in a suddenly displaced delta potential, including novel insights into its movement probabilities and spectral dynamics.

Findings

Fraction of wavefunction remains confined during potential displacement

Existence of a probability for the particle to move at double speed

Spectral and temporal dynamics characterized for different scenarios

Abstract

We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wavefunction remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.