Similarity Analytical Solutions for the Schrӧdinger Equation with the
Riesz Fractional Derivative in Quantum Mechanics
Abstract
The present article deals with the similarity method to tackle the
fractional Schrӧdinger 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 .