Quantum particles in a suddenly moving localized potential

TL;DR

This paper investigates the quantum dynamics of particles in localized potentials that suddenly start moving, extending previous work to various potentials including the hydrogen atom, and calculates ionization probabilities.

Contribution

It introduces a spectral decomposition approach to analyze quantum particles in moving potentials, applying it to multiple potential types including the hydrogen atom.

Findings

Reproduced known results for delta potentials using spectral methods.

Extended analysis to P"oschl-Teller, harmonic oscillator, and hydrogen atom potentials.

Calculated explicit ionization probability for hydrogen atom due to sudden potential movement.

Abstract

We study the behavior of a quantum particle, trapped in localized potential, when the trapping potential starts suddenly to move with constant velocity. In one dimension we have reproduced the results obtained by Granot and Marchewka, Ref. \cite{Granot09}, for an attractive delta function, using an approach based on a spectral decomposition, rather than on the propagator. We have also considered the cases of P\"oschl-Teller and simple harmonic oscillator potentials (in one dimension) and to the hydrogen atom (in three dimensions). In this last case we have calculated explicitly the leading contribution to the ionization probability for the hydrogen atom due to a sudden movement.