Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1634-1642.

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δ-Potential in Space-Time Fractional Quantum Mechanics

Ying Lu,Yunjie Tan,Jianping Dong*()   

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106
  • Received:2020-08-07 Online:2021-12-26 Published:2021-12-02
  • Contact: Jianping Dong
  • Supported by:
    the NSFC(11701278);the Fundamental Research Funds for the Central Universities(NZ2019008)


Space-time fractional quantum mechanics, described by Schrödinger equation with Caputo derivative and Riesz derivative, is a generalization of quantum mechanics and can depict more extensive quantum phenomena. This paper studies the one-dimensional space-time fractional Schrödinger equation for a particle in the single and double δ-potential well, and gives the wave functions and energy levels of the particle. In addition, the space-time fractional quantum mechanical path integrals kernels of a particle in the δ-potential well are established by using integral transformation, and the corresponding Fox's H-function forms are derived, and the relation between space-time fractional Schrodinger equation and path integrals is constructed. It provides more possibilities to study space-time fractional quantum mechanics from the perspective of path integrals.

Key words: Space-time fractional Schrödinger equation, Quantum mechanical kernel, Fox's H-function

CLC Number: 

  • O29