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A fractional schrödinger equation and its solution

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2010

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Springer/Plenum Publishers

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Abstract

This paper presents a fractional Schrodinger equation and its solution. The fractional Schrodinger 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 Schrodinger equation of order alpha. We also use a fractional Klein-Gordon equation to obtain the fractional Schrodinger 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

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Lagrangian and Hamiltonian Approach

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Muslih, S.I., Baleanu, D., Agrawal, O.P. (2010). A fractional schrödinger equation and its solution. International Journal of Theoretical Physics, 49(8), 1746-1752. http://dx.doi.org/ 10.1007/s10773-010-0354-x

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Source

International Journal of Theoretical Physics

Volume

49

Issue

8

Start Page

1746

End Page

1752