Similarity Analytical Solutions for the Schrodinger Equation with the Riesz Fractional Derivative in Quantum Mechanics

TL;DR

This paper introduces a similarity method to solve the fractional Schrödinger equation with Riesz derivatives, transforming it into ODEs for easier analysis and providing graphical solutions for various fractional derivatives.

Contribution

It presents a novel approach to reduce fractional PDEs to ODEs using scaled transforms and Fourier analysis, specifically applied to the fractional Schrödinger equation with Riesz derivatives.

Findings

Effective reduction of fractional PDEs to ODEs

Graphical solutions for different fractional derivatives

Enhanced understanding of fractional quantum mechanics

Abstract

The present article deals with the similarity method to tackle the fractional Schrodinger equation where the derivative is defined in the Riesz sense. Moreover the procedure of reducing a fractional partial differential equation (FPDE) into an ordinary differential equation (ODE) has been efficiently displayed by means of suitable scaled transform to the proposed fractional equation. Furthermore the ODEs are treated effectively via the Fourier transform. The graphical solutions are also depicted for different fractional derivatives .