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

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.

MARWAN AL-RAEEI¹ MOUSTAFA SAYEM EL-DAHER^{2 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

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