arXiv:1009.5533math-ph
Principles of Fractional Quantum Mechanics
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Abstract
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schrödinger 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 δ-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the Lévy path integral approach to fractional statistical mechanics.
Here's a well-explained article about fractional derivatives and integrals (1). One freaky outcome is that the factorials of fractional numbers can be found. (Example: negative one half factorial = square root of pi.) It can be applied to all things quantum mechanical (2) so…
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