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Fractional Schrödinger equation

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2002 · Vol. 66(5) · pp. 056108–056108

Nick Laskin✉(University of Toronto)

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Abstract

Some properties of the fractional Schrödinger 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 Schrödinger 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 Schrödinger equations.

Fractional Differential Equations Solutions Statistical Mechanics and Entropy Quantum Mechanics and Non-Hermitian PhysicsBohr modelSemiclassical physicsSchrödinger equationFractional calculusMathematical physicsPhysicsQuantum mechanicsOperator (biology)MathematicsQuantum

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