Similarity analytical solutions for the Schrӧdinger equation with the Riesz fractional derivative in quantum mechanics
Asim Patra
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 α .
Topics & Concepts
MathematicsOdeFractional calculusSimilarity (geometry)Ordinary differential equationPartial differential equationMathematical analysisFourier transformDerivative (finance)Differential equationApplied mathematicsImage (mathematics)Computer scienceEconomicsArtificial intelligenceFinancial economicsFractional Differential Equations SolutionsQuantum Mechanics and Non-Hermitian PhysicsNonlinear Waves and Solitons