FRACTIONAL CALCULUS AND THE SCHRÖDINGER EQUATION

In this paper, a derivation of the fractional Schrödinger equation is presented for the simple case of a pure diffusive process with dissipation. The Gaussian white noise is replaced by more general kinds of white noise and both the Markovian both the Markovian (β = 1) and non-Markovian case (0 < β < 1) are considered.