分数维空间中的分数阶双δ-势
Fractional Double δ-Potential in Fractional Dimensional Space
DOI: 10.12677/MP.2021.114011, PDF,    国家自然科学基金支持
作者: 谭云杰, 董建平*：南京航空航天大学理学院，江苏 南京；陈益隆：埃默里大学埃默里艺术与科学学院，美国 亚特兰大
关键词: 分数维空间；分数阶薛定谔方程；Fox’s H函数；分数双δ-势；Fractional Dimension Space； Fractional Schr?dinger Equation； Fox’s H Function； Fractional Double δ-Potential
摘要: 本文主要研究分数维空间中的分数阶量子力学问题，考虑了 维空间中含Riesz分数导数的分数阶薛定谔方程，利用分数维空间中的傅里叶变换，求解了分数维空间中的分数阶双δ-势的分数阶薛定谔方程，得到了含有Fox’s H函数形式的波函数以及能量本征值。此外，本文利用Fox’s H函数的性质研究了波函数在自变量及双δ-势间隔a在趋于零和无穷时的渐进性质，给出了具体的渐进表达式，发现在两种无穷趋势下波函数的性态都是含空间维数 的负幂律函数，揭示了空间维数与波函数、分数阶微积分与负幂律间的紧密联系。
Abstract: In this paper, we study the fractional-order quantum mechanics problems in the fractional dimen-sional space. The fractional Schrödinger equation with Riesz fractional derivative in dimensional space is considered. By using the Fourier transform in the fractional dimensional space, the fractional Schrödinger equation with fractional double δ-potential well in fractional dimensional space is solved and obtained the wave function with the form of Fox’s H functions and the energy eigenvalue. In addition, by using the properties of Fox’s H functions, we study the asymptotic properties of the wave function when the independent variable and the double delta potential interval a tending to zero and infinity, and give the specific asymptotic expressions. It is found that the behavior of wave function is a negative power law function that contains space di-mension under two kinds of infinite trends, the close relationship between space dimension and wave function, fractional calculus and negative power law is revealed.
文章引用：谭云杰, 陈益隆, 董建平. 分数维空间中的分数阶双δ-势[J]. 现代物理, 2021, 11(4): 80-87. https://doi.org/10.12677/MP.2021.114011

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