Plateaux of probability for the expanded quantum infinite well

TL;DR

This paper introduces a mathematical framework to explain the occurrence of probability plateaux at fractional times during the evolution of an expanded quantum infinite well, revealing connections to number theory.

Contribution

It provides a novel mathematical explanation for probability plateaux in quantum wells, linking quantum dynamics to number theory considerations.

Findings

Probability plateaux occur at fractional times during quantum well expansion.

The characterization of these plateaux involves nontrivial number theoretical analysis.

The framework explains previously observed phenomena in quantum dynamics.

Abstract

If the standard 1D quantum infinite potential well initially in its ground state suffers a sudden expansion, it turns out that in the evolution of the system they may appear plateaux of probability for some fractional times, as noticed by C. Aslangul in 2008. We introduce a mathematical framework to explain this phenomenon. Remarkably, the characterization of these plateaux depends on nontrivial number theoretical considerations.