Small perturbations leading to large asymmetries in the probability density of the ground state

TL;DR

This paper demonstrates that minor changes in a one-dimensional quantum potential can cause significant asymmetries in the ground state probability density, challenging standard perturbation theory assumptions.

Contribution

It reveals a non-standard effect where small potential perturbations lead to large ground state asymmetries, with implications for solid state physics and related fields.

Findings

Small perturbations cause large asymmetries in ground state density.

Effect intensifies with increasing potential length.

Examples of non-standard perturbations are provided.

Abstract

It is shown that in one-particle Schr\"{o}dinger quantum mechanics a small perturbation of a one-dimensional potential can produce a large change in the ground state, the effect becoming more pronounced with growing typical length of the potential, contrary to what standard stationary perturbation theory could make one believe.The possible consequences of this result for solid state physics and other fields are also discussed, and examples of such non-standard perturbations are furnished.