Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918197041561600 |
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| author | Pereira, Matheus E. Schmidt, Alexandre G. M. |
| author_facet | Pereira, Matheus E. Schmidt, Alexandre G. M. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates Pereira, Matheus E. Schmidt, Alexandre G. M. Quantum Physics 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. |
| title | Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.08646 |