2007/07/01 by Jianping Dong, Mingyu Xu · 141 citations
Mathematics · Physics and Astronomy · #Bound state #Coulomb #Coulomb wave function #Electron #Fourier transform #Fractional Differential Equations Solutions #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Waves and Solitons #Parity (physics) #Physics #Position and momentum space #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger equation #Wave function
paper · doi:10.1063/1.2749172
published in Journal of Mathematical Physics 48(7) (American Institute of Physics)
openalex publication_date 2007/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The space fractional Schrödinger equation with linear potential, delta-function potential, and Coulomb potential is studied under momentum representation using Fourier transformation. By use of Mellin transform and its inverse transform, we obtain the energy levels and wave functions expressed in H function for a particle in linear potential field. The wave function expressed also by the H function and the unique energy level of the bound state for the particle of even parity state in delta-function potential well, which is proved to have no action on the particle of odd parity state, is also obtained. The integral form of the wave functions for a particle in Coulomb potential field is shown and the corresponding energy levels which have been discussed in Laskin’s paper [Phys. Rev. E 66, 056108 (2002)] are proved to satisfy an equality of infinite limit of the H function. All of these results contain the ones of the standard quantum mechanics as their special cases.