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<p>We consider the three-dimensional stationary Schrödinger equation deformed by Dunkl operators, and constrained to the surface of a torus. After separation of variables in toroidal coordinates, it is shown that the Schrödinger equation admits solutions in terms of Heun functions, provided the potential has a certain form. As an application, elementary solutions of bound-state type are constructed that are expressed through Heun polynomials.</p>

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THE DUNKL-SCHRÖDINGER EQUATION ON THE TORUS: SOLVABLE CASES AND BOUND STATES

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  • 发表日期：

    2026年3月14日

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  • Axel Schulze-Halberg

摘要

We consider the three-dimensional stationary Schrödinger equation deformed by Dunkl operators, and constrained to the surface of a torus. After separation of variables in toroidal coordinates, it is shown that the Schrödinger equation admits solutions in terms of Heun functions, provided the potential has a certain form. As an application, elementary solutions of bound-state type are constructed that are expressed through Heun polynomials.