A simple example of pressure excitation:the 3D square well potential

TL;DR

This paper uses the 3D square well potential to model how high external pressure causes discrete energy level transitions and particle expulsion, providing a simple quantum mechanical example relevant to high-pressure physics.

Contribution

It introduces a solvable quantum model demonstrating pressure-induced energy level transitions and particle ejection, linking quantum mechanics with high-pressure phenomena.

Findings

Discrete pressure values induce energy level transitions.

Pressure can expel particles from the potential well.

Model illustrates pressure effects in a simple quantum system.

Abstract

High pressure experiments in diamond anvil cells as well as in geophysics show that at certain discrete values of pressure abrupt changes of the mass density and changes of the material structure occur. The aim of this paper is to discuss the influence of high external pressure on atoms and molecules using the $3D$ square well potential as a simple solvable quantum mechanical example. Values of external pressure needed for a transition between energy levels with different values of the main quantum number $n$, as well as the pressure needed to expel the particle from this system are calculated. In both cases discrete values of pressure are obtained.