Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 45, Issue 8, Pages 3339-3352Publisher
AMER INST PHYSICS
DOI: 10.1063/1.1769611
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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 nonlocal 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. (C) 2004 American Institute of Physics.
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