Fractional Schrodinger equation

Some properties of the fractional Schrodinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we find the energy spectra of a hydrogenlike atom (fractional Bohr atom) and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrodinger equations.