无限深方势阱中分数阶量子力学核的变换  

Transformation of Fractional Quantum Mechanical Kernel in the Infinite Square Well

作　　者：陆莹 董建平 

机构地区：[1]南京航空航天大学理学院,江苏 南京

出　　处：《现代物理》2020年第5期79-85,共7页Modern Physics

摘　　要：分数阶量子力学核是一种波函数,它可以描述分数阶量子系统的演化过程。本文研究无限深方势阱中自由粒子量子力学核的Laplace变换、能量–时间变换和动量表示。我们首先借助无限深方势阱中自由粒子量子力学核的Fox’s H函数表示,得到量子力学核的Laplace变换。然后利用量子力学核的路径积分形式,计算出它的能量–时间变换和动量表示。量子力学核的变换可以简化分数阶量子力学中的计算结果,从而更好地研究其性质。Fractional quantum mechanics kernel is a kind of wave function, which can describe the evolution process of fractional quantum system. In this paper, we study the Laplace transformation, ener-gy-time transformation and momentum representation of free particle quantum mechanics kernel in infinite square well. Firstly, we obtain the Laplace transformation of quantum mechanical kernel by using the Fox’s H function representation of free particle quantum mechanics kernel in the infinite square well, and then use Path integral form of quantum mechanics kernel to calculate its energy-time transformation and momentum representation. The transformation of quantum me-chanics kernel can simplify the calculation results in fractional quantum mechanics, so as to study its properties better.

关 键 词：分数阶量子力学核 积分变换 Fox’s H函数 

分 类 号：O41[理学—理论物理]