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arXiv · 2504.08311

On the SUSY structure of spherically symmetric Pauli Hamiltonians

Georg Junker
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Abstract

It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar potentials and spherical symmetric vector potentials are discussed in detail. The current approach, which includes the spin-1/2 degree of freedom, provides new insights to known models like the radial harmonic oscillator and the Coulomb problem. We also find a few new exactly solvable models, one of them exhibiting a new mixed type of shape invariance containing translation and scaling of potential parameters. The fundamental role as Witten parity played by the spin-orbit operator is high-lighted.

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Georg Junker. 2025-04-11. On the SUSY structure of spherically symmetric Pauli Hamiltonians. https://doi.org/10.1007/s00601-025-01994-w

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