Year: 2026
Type: preprint
Abstract: Separation of variables in Schrödinger equation allows an infinite-dimensional family of physically distinct field configurations that are dynamically indistinguishable in one selected sector, labeled by a conserved quantum number, while differing in all others. We call such a symmetry a partial isophase symmetry. Two main examples are considered: axially symmetric magnetic backgrounds (a rigid spectral flow of the Fock--Darwin oscillator, purely magnetic isophase families, and a two-channel extension) and a Cartesian slab geometry (magnetic barriers in two-dimensional electron gases, treated in the Appendices). We further discuss the consequences of this symmetry for the inverse spectral problem and consider its quasiclassical counterpart.
Source: arXiv (Cornell University)
Author: Pupasov-Maksimov, Andrey M.
Institution: Universidade Federal de Juiz de Fora
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222952026