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<p>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-<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1994_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation> 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.</p>

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On the SUSY Structure of Spherically Symmetric Pauli Hamiltonians

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月18日

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  • Georg Junker

摘要

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- \(\frac{1}{2}\) 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.