Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints
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...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/137 |
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| author | Irina Petreska Pece Trajanovski Trifce Sandev Jonathan A. M. Almeida Rocha Antonio Sérgio Magalhães de Castro Ervin K. Lenzi |
| author_facet | Irina Petreska Pece Trajanovski Trifce Sandev Jonathan A. M. Almeida Rocha Antonio Sérgio Magalhães de Castro Ervin K. Lenzi |
| author_sort | Irina Petreska |
| collection | DOAJ |
| description | 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 <i>H</i>-functions. |
| format | Article |
| id | doaj-art-614a1f735b7b41bdb7c8d9813b4b90bb |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-614a1f735b7b41bdb7c8d9813b4b90bb2025-01-10T13:18:21ZengMDPI AGMathematics2227-73902025-01-0113113710.3390/math13010137Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric ConstraintsIrina Petreska0Pece Trajanovski1Trifce Sandev2Jonathan A. M. Almeida Rocha3Antonio Sérgio Magalhães de Castro4Ervin K. Lenzi5Institute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, MacedoniaInstitute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, MacedoniaInstitute of Physics, Faculty of Natural Sciences and Mathematics— Skopje, Ss. Cyril and Methodius University in Skopje, Arhimedova 3, 1000 Skopje, MacedoniaDepartamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, BrazilDepartamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, BrazilDepartamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, BrazilHere, 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 <i>H</i>-functions.https://www.mdpi.com/2227-7390/13/1/137time-dependent 3D Schrödinger equationnonlocal interactionsquantum dynamicsGreen’s functions |
| spellingShingle | Irina Petreska Pece Trajanovski Trifce Sandev Jonathan A. M. Almeida Rocha Antonio Sérgio Magalhães de Castro Ervin K. Lenzi Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints Mathematics time-dependent 3D Schrödinger equation nonlocal interactions quantum dynamics Green’s functions |
| title | Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints |
| title_full | Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints |
| title_fullStr | Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints |
| title_full_unstemmed | Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints |
| title_short | Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints |
| title_sort | solutions to the schrodinger equation nonlocal terms and geometric constraints |
| topic | time-dependent 3D Schrödinger equation nonlocal interactions quantum dynamics Green’s functions |
| url | https://www.mdpi.com/2227-7390/13/1/137 |
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