Time fractional Schrodinger equation

Details Time fractional Schrodinger equation Time fractional Schrodinger equation

2004-10-10

arxiv.org/abs/math-ph/0410028v1

J. Math. Phys. Vol 45, No. 8 pages 3339-3352, Aug. 2004

Physics

Mathematical Physics

23 pages

Scientific paper

10.1063/1.1769611

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrodinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag-Leffler function are also found and presented in an appendix.

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