An algorithm for fractional Schrodinger equation in case of Morse potential

Based on methods of numerical integration and Riemann-Liouville definition of the fractional derivatives, we find a numerical algorithm to find solutions of the time independent fractional Schrodinger equation for Morse potential or the quantum oscillator potential in one dimension, and the iteration formula is applied for multiple values of the fractional parameter of the space dependent fractional Schrodinger equation and multiple values of energy. We define and use the dimensionless form of the space dependent fractional Schrodinger equation of Morse potential. We employ the iteration formula of the time independent fractional Schrodinger equation of Morse potential to find the wave functions in the case of hydrogen chloride and hydrogen fluoride molecules for a certain value of the fractional parameter of the space dependent fractional Schrodinger equation and for many values of the dimensionless energy of each molecule. (c) 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).