2014/07/14 by A. Davidson, Arthur Davidson, Davidson, Arthur
Engineering · Physics and Astronomy · #FOS: Physical sciences #Mechanical and Optical Resonators #Nonlinear Photonic Systems #Photonic and Optical Devices #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1407.3826
11 pages, 1 figure, new: gauge invariance argument now uses de Broglie relation
openalex publication_date 2014/07/14 · arxiv created 2015/01/08 · arxiv updated 2015/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Remarkably we find that for a ring with linear boundary conditions such that the eigenvector and its derivative are continuous, there does not seem to be a way for the well-known de Broglie relation to be gauge invariant. Certain nonlinear boundary conditions assure gauge invariance, and lead to eigenfunctions with a discontinuous but differentiable phase and a continuous spectrum. A discrete subset of this spectrum forms a Hilbert space, while another subset is excluded by the nonlinear boundaries. We conclude that discontinuous momentum eigenfunctions are tenable, and that it is possible that quantum mechanics can have nonlinear boundary conditions in some circumstances.