Distributed Phase Acquisition in a Wave Function

TL;DR

This paper investigates how an electron's wave function acquires phase during adiabatic electromagnetic interactions in a confined system, revealing cyclic degeneracies and phase evolution in quantum states.

Contribution

It introduces a model demonstrating phase acquisition in a wave function due to adiabatic electromagnetic fields, highlighting cyclic degeneracies in quantum systems.

Findings

Adiabatic solutions show gradual phase acquisition in wave functions.

Cyclic motion of the source leads to co-degenerate wave functions.

The model applies to a specific vector potential with no magnetic fields.

Abstract

A separable $x-y$ model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly\textbf{,} adiabatically into and across a rectangular box to which an electron is confined. The time-dependent Schr\"odinger equation has adiabatic solutions, in which gradual phase acquisitions occur for {\it parts} of the electronic wave function. For a closed trajectory of the source, the initial and after-return wave functions are shown to be simultaneously co-degenerate solutions of the Hamiltonian, which situation repeats itself for further cyclic motion of the source.