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Title: Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Authors: Saxena, R.
Saxena, Ravi
Kalla, S.
Keywords: Mittag-Leffler Function
Quantum Mechanics
Fourier Transform
Fractional Schrödinger Equation
Caputo Derivative
Levy Distribution
Feynman Path Integrals
Gaussian Probability Distribution
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 13, No 2, (2010), 177p-190p
Abstract: The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant extension of a result given earlier by Debnath, and by Saxena et al. The main result is obtained in the form of Theorem 1. Three special cases of this theorem are given as corollaries. Computational representation of the fundamental solution of the proposed equation is also investigated.
Description: Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.
ISSN: 1311-0454
Appears in Collections:2010

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