分数阶量子力学下的二维无限深方势阱  

Two-Dimensional Infinite Square Well in Fractional Quantum Mechanics

作　　者：谭云杰 韩小惠 董建平[1,2] Tan Yunjie;Han Xiaohui;Dong Jianping(College of Mathematics,Nanjing University of Aeronautics and Astronautics,Najing 211106;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MHT,Najing 211106)

机构地区：[1]南京航空航天大学数学学院,南京211106 [2]飞行器数学建模与高性能计算工业和信息化部重点实验室南京航空航天大学,南京211106

出　　处：《数学物理学报（A辑）》2022年第4期1018-1026,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701278);中央高校基本科研业务费专项资金(NZ2019008)。

摘　　要：分数阶量子力学是标准量子力学的一种推广,由包含分数阶Riesz导数的空间分数阶Schrodinger方程所描述.该文考虑了在二维无限深方势阱中运动的自由粒子,利用Lévy路径积分传播子,得到了在二维无限深方势阱内运动粒子的波函数和能量本征值.此外,运用Lévy路径积分摄动技术,得到了在δ函数摄动下的二维无限深方势阱区域内运动粒子的能量依赖格林函数.Fractional quantum mechanics is a generalization of standard quantum mechanics,which is described by fractional Schrodinger 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 withδfunction,and the corresponding energy-dependent Green’s function is obtained.

关 键 词：分数阶Schrodinger方程 Lévy路径积分 传播子 无限深方势阱 

分 类 号：O174.3[理学—数学]