Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Saxena, R., Saxena, Ravi, and Kalla, S.. "Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics." Fractional Calculus and Applied Analysis 13.2 (2010): 177-190. <http://eudml.org/doc/219529>.

@article{Saxena2010,
abstract = {Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.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.},
author = {Saxena, R., Saxena, Ravi, Kalla, S.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Mittag-Leffler Function; Quantum Mechanics; Fourier Transform; H-Function; Fractional Schrödinger Equation; Caputo Derivative; Levy Distribution; Feynman Path Integrals; Gaussian Probability Distribution; Mittag-Leffler function; quantum mechanics; Fourier transform; -function; fractional Schrödinger equation; Caputo derivative; Lévy distribution; Feynman path integrals; Gaussian probability distribution},
language = {eng},
number = {2},
pages = {177-190},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics},
url = {http://eudml.org/doc/219529},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Saxena, R.
AU - Saxena, Ravi
AU - Kalla, S.
TI - Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 2
SP - 177
EP - 190
AB - Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.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.
LA - eng
KW - Mittag-Leffler Function; Quantum Mechanics; Fourier Transform; H-Function; Fractional Schrödinger Equation; Caputo Derivative; Levy Distribution; Feynman Path Integrals; Gaussian Probability Distribution; Mittag-Leffler function; quantum mechanics; Fourier transform; -function; fractional Schrödinger equation; Caputo derivative; Lévy distribution; Feynman path integrals; Gaussian probability distribution
UR - http://eudml.org/doc/219529
ER -