分数阶量子力学下的二维无限深方势阱

Abstract

Abstract:

Fractional quantum mechanics is a generalization of standard quantum mechanics, which is described by fractional Schrödinger equation with fractional Riesz derivative operator. In this paper, we consider a free particle moving in a two-dimensional infinite square well, By using Lévy path integral method, the wave function and energy eigenvalue of the two-dimensional infinite square well are obtained. Then the perturbation expansion method is used to study the two-dimensional infinite square well with $\delta$ function, and the corresponding energy-dependent Green's function is obtained.

Key words: Fractional Schrödinger equation, Lévy path integral, Propagator, Infinite square well

CLC Number:

O174.3

Yunjie Tan,Xiaohui Han,Jianping Dong. Two-Dimensional Infinite Square Well in Fractional Quantum Mechanics[J].Acta mathematica scientia,Series A, 2022, 42(4): 1018-1026.

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References 29

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[2]	Wenbo Wang,Quanqing Li. Existence and Concentration of Nontrivial Solutions for the Fractional Schrödinger Equations with Sign-Changing Steep Well Potential [J]. Acta mathematica scientia,Series A, 2018, 38(5): 893-902.
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Two-Dimensional Infinite Square Well in Fractional Quantum Mechanics

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