Partially isophase electro-magnetic configurations

arXiv:2610.23645v1 Announce Type: new Abstract: Separation of variables in Schr\"{o}dinger 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.