prof. dr hab. Włodzimierz Stefanowicz, IF UO

Fractional quantum mechanics and confining potentials for Levy flights.

Levy flight is non-Gaussian stochastic process having probability density function (PDF) slowly (as compared to Gaussian) decaying at infinities. This yields the divergent second moments of corresponding PDF. To make Levy flights be usable in real physical systems, we need to make their higher moments existent. For that suitably tailored (dictated by specific physical problem) external potentials are used. Here we discuss different confining mechanisms, met in real physical systems. One of them is so-called fractional quantum mechanics, when ordinary Laplacian in the Schrodinger equation is substituted by the fractional derivative. We discuss the method of solution of fractional quantum mechanical problems.