International Journal of Theoretical Physics

, Volume 49, Issue 8, pp 1746–1752 | Cite as

A Fractional Schrödinger Equation and Its Solution

Article

Abstract

This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.

Keywords

Lagrangian and Hamiltonian approach 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Sami I. Muslih
    • 1
  • Om P. Agrawal
    • 1
  • Dumitru Baleanu
    • 2
  1. 1.Department of Mechanical EngineeringSouthern Illinois UniversityCarbondaleUSA
  2. 2.Department of Mathematics and Computer Sciences, Faculty of Arts and SciencesÇankaya UniversityAnkaraTurkey

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