Re-Thinking Schroedinger Boundary Conditions: the Simple Rotator is Not Simple

TL;DR

This paper proposes new gauge-invariant boundary conditions for the quantum rotator, challenging standard assumptions and impacting energy flow analysis, with implications beyond the specific problem.

Contribution

It introduces a novel approach to boundary conditions in quantum mechanics that are gauge-invariant and broadly applicable.

Findings

Standard boundary conditions lead to contradictions in simple rotator models.

New gauge-invariant boundary conditions resolve these contradictions.

Implications for energy flow in quantum systems are significant.

Abstract

A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and that can be applied beyond the immediate problem. The use of gauge invariant boundary conditions has important consequence for energy flow in or out of a simple rotator.