Autocorrelation function in time-fractional quantum mechanics

Abstract

A general expression for the autocorrelation function in time-fractional quantum mechanics is derived in terms of a Mittag-Leffler function. As a special case, the autocorrelation function over a small time interval, for zero-momentum wave packets in the 1D infinite well is investigated. It is observed that when considering the time-fractional case, certain values for the autocorrelation after some time, t > 0 are greater than the initial value, a consequence attributed to the unnormalized probability in Naber’s time-fractional formulation.