Fractional Schrodinger equation

Details Fractional Schrodinger equation Fractional Schrodinger equation

2002-06-14

arxiv.org/abs/quant-ph/0206098v1

Phys.Rev.E66:056108,2002

Physics

Quantum Physics

18 pages

Scientific paper

10.1103/PhysRevE.66.056108

Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we have found the energy spectrum for a hydrogen-like atom - fractional ''Bohr atom'' and the energy spectrum of fractional oscillator in the semiclassical approximation. A new equation for the fractional probability current density has been developed and discussed. We also discuss the relationships between the fractional and the standard Schrodinger equations.

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