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    • An iteration algorithm for the time-independent fractional Schrödinger equation with Coulomb potential

      MARWAN AL-RAEEI MOUSTAFA SAYEM EL-DAHER

      Research Article Volume 94 Published: 29 October 2020 Article ID 0157

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      https://www.ias.ac.in/article/fulltext/pram/094/0157

    • Keywords

       

      Fractional Schrödinger equation; Liouville–Riemann definition; Coulomb potential; fractional parameter; fractional Bohr’s atom formula

    • Abstract

       

      A numerical formula is derived which gives solutions of the fractional Schrödinger equation in time-independent form in the case of Coulomb potential using Riemann–Liouville definition of the fractional derivative and the quadrature methods. The formula is applied for electron in the nucleus field for multiple values of fractional parameter of the space-dependent fractional Schrödinger equation and for each value of the space-dependent fractional parameter, multiple values of energies are applied. Distances are found at which the probability takes its maximum value. Values of energy obtained in this study corresponding to the maximum value of probability are compared with the energy values resulted from the fractional Bohr’s atom formula in the fractional quantum mechanics.

    • Author Affiliations

       

      MARWAN AL-RAEEI1 MOUSTAFA SAYEM EL-DAHER2 3

      1. Physics Department, Faculty of Sciences, Damascus University, Damascus, Syria
      2. Higher Institute of Laser Applications and Researches, Damascus University, Damascus, Syria
      3. Faculty of Informatics and Communications, Arab International University, Daraa, Syrian Arab Republic

    • Dates

       
      Published
      29 October 2020
      Manuscript received
      9 April 2020
      Manuscript revised
      5 July 2020
      Accepted
      18 August 2020
      Final version published online
      28 October 2020

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      Posted on July 25, 2019

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