Some physical applications of fractional Schrödinger equation

The fractional Schrodinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schrodinger equation, the Green’s function of the Lippmann-Schwinger integral equation is given.