Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints

被引：2

作者：

Petreska, Irina ^{[1
]}

Trajanovski, Pece ^{[1
,2
]}

Sandev, Trifce ^{[1
,2
,3
]}

Rocha, Jonathan A. M. Almeida ^{[4
]}

de Castro, Antonio Sergio Magalhaes ^{[4
]}

Lenzi, Ervin K. ^{[4
,5
]}

机构：

[1] Ss Cyril & Methodius Univ Skopje, Fac Nat Sci & Math Skopje, Inst Biol, Arhimedova 3, Skopje 1000, North Macedonia

[2] Macedonian Acad Sci & Arts, Res Ctr Comp Sci & Informat Technol, Bul Krste Misirkov 2, Skopje 1000, North Macedonia

[3] Korea Univ, Dept Phys, Seoul 02841, South Korea

[4] Univ Estadual Ponta Grossa, Dept Fis, Ave Carlos Cavalcanti 4748, BR-84030900 Ponta Grossa, PR, Brazil

[5] Univ Estadual Maringa, Dept Fis, Ave Colombo 5790, BR-87020900 Maringa, PR, Brazil

来源：

MATHEMATICS | 2025年 / 13卷 / 01期

关键词：

time-dependent 3D Schr & ouml; dinger equation; nonlocal interactions; quantum dynamics; Green's functions; ANOMALOUS DIFFUSION; FRACTIONAL CALCULUS;

D O I：

10.3390/math13010137

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here, we investigate a three-dimensional Schr & ouml;dinger 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 Schr & ouml;dinger equation with a nonlocal dependence governed by short- or long-tailed distributions characterized by power laws associated with L & eacute;vy 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.

引用

页数：13

共 52 条

[1] Colloquium: Anomalous statistics of laser-cooled atoms in dissipative optical lattices [J].