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Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints

Author

Listed:
  • Irina Petreska

    (Institute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, Macedonia)

  • Pece Trajanovski

    (Institute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, Macedonia
    Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia)

  • Trifce Sandev

    (Institute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, Macedonia
    Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
    Department of Physics, Korea University, Seoul 02841, Republic of Korea)

  • Jonathan A. M. Almeida Rocha

    (Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil)

  • Antonio Sérgio Magalhães de Castro

    (Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil)

  • Ervin K. Lenzi

    (Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil
    Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá 87020-900, PR, Brazil)

Abstract

Here, we investigate a three-dimensional Schrödinger equation that generalizes the standard framework by incorporating geometric constraints. Specifically, the equation is adapted to account for a backbone structure exhibiting memory effects dependent on both time and spatial position. For this, we incorporate an additional term in the Schrödinger equation with a nonlocal dependence governed by short- or long-tailed distributions characterized by power laws associated with Lévy distributions. This modification also introduces a backbone structure within the system. We derive solutions that reveal various behaviors using Green’s function approach expressed in terms of Fox H -functions.

Suggested Citation

  • Irina Petreska & Pece Trajanovski & Trifce Sandev & Jonathan A. M. Almeida Rocha & Antonio Sérgio Magalhães de Castro & Ervin K. Lenzi, 2025. "Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints," Mathematics, MDPI, vol. 13(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:137-:d:1558329
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