# Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime

## TL;DR

This paper investigates the non-adiabatic quantum dynamics of a hydrogen-like atom confined in a time-dependent spherical box, analyzing how rapid boundary movements affect the atom's energy states and electron behavior.

## Contribution

It introduces a model of a hydrogen atom in a dynamically changing spherical confinement, exploring non-adiabatic effects on atomic energy and electron states during rapid boundary movements.

## Key findings

- Linearly expanding box causes atomic de-excitation.
- Rapid contraction induces high pressure and ionization.
- Harmonic breathing leads to diffusive excitation similar to microwave fields.

## Abstract

We consider a hydrogen atom confined in time-dependent trap created by a spherical impenetrable box with time-dependent radius. For such model we study the behavior of atomic electron under the (non-adiabatic) dynamical confinement caused by the rapidly moving wall of the box. The expectation values of the total and kinetic energy, average force, pressure and coordinate are analyzed as a function of time for linearly expanding, contracting and harmonically breathing boxes. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron may occur in analogy with that for atom in a microwave field.