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reviewer cc MSC code ut uncontrolled term Time fractional
Schrödinger equation. (English) Zbl 1071.81035 Summary: The
Schrödinger equation is considered with the first order time
derivative changed to a Caputo fractional derivative, the time
fractional Schrödinger 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 Schrödinger 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 a