Related papers: Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates

Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates

URL: http://arxiv.org/abs/2511.08646v1
Date: Thu, 13 Nov 2025 01:01:25 GMT
Title: Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates
Authors: Matheus E. Pereira, Alexandre G. M. Schmidt,
Abstract summary: We present, for the first time, exact solutions for the Schrdinger equation in Moon and Spencer's toroidal coordinates.<n>We achieve these novel solutions using the irregular $mathcalR$-separation of variables.
Score: 45.88028371034407
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We present, for the first time, exact solutions for the Schrödinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional angular momentum, because of the torus's hole. We achieve these novel solutions using the irregular $\mathcal{R}$-separation of variables, an unexplored approach in Physics, which results in a wavefunction with fractional angular momentum eigenvalues. Numerous solutions for the Schrödinger equation in a variety of external potentials are shown, including an external magnetic field. A plane-wave expansion and a Green function are also presented, setting the stage for future progress in this area.

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