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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08646 |
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Table of Contents:
- 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.