Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints

Irina Petreska, Pece Trajanovski, Trifce Sandev, Jonathan A. M. Almeida Rocha, Antonio Sérgio Magalhães de Castro and Ervin K. Lenzi ()
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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
Trifce Sandev: Institute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, Macedonia
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

Mathematics, 2025, vol. 13, issue 1, 1-13

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.

Keywords: time-dependent 3D Schrödinger equation; nonlocal interactions; quantum dynamics; Green’s functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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