Principles of Fractional Quantum Mechanics

Details Principles of Fractional Quantum Mechanics Principles of Fractional Quantum Mechanics

2010-09-28

arxiv.org/abs/1009.5533v1

Physics

Mathematical Physics

31 pages

Scientific paper

A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\'evy path integral approach to fractional statistical mechanics.

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