Computational solution of a fractional generalization of the Schrödinger equation occurring in quantum mechanics

DOI10.1016/J.AMC.2010.02.041zbMath1190.65157OpenAlexW2075009970MaRDI QIDQ972914

B. E. Eshmatov

Publication date: 21 May 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.02.041

zbMATH Keywords

Mittag-Leffler functionSchrödinger equationquantum mechanicsCaputo derivativefractional generalizationjoint Laplace and Fourier transforms

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) PDEs in connection with quantum mechanics (35Q40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (10)

The fractional dynamics of quantum systems ⋮ Distributed order reaction-diffusion systems associated with Caputo derivatives ⋮ Space-time fractional Schrödinger equation with composite time fractional derivative ⋮ Shehu transform on time-fractional Schrödinger equations -- an analytical approach ⋮ Analytical solution of the space-time fractional nonlinear Schrödinger equation ⋮ On the solutions for generalised multiorder fractional partial differential equations arising in physics ⋮ Lévy Transport in Slab Geometry of Inhomogeneous Media ⋮ Analytic and approximate solutions of the space-time fractional Schrödinger equations by homotopy perturbation Sumudu transform method ⋮ Solutions of unified fractional Schrödinger equations ⋮ Computational solutions of distributed order reaction-diffusion systems associated with Riemann-Liouville derivatives

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