Principles of Fractional Quantum Mechanics
Mathematical Physics
2010-09-29 v1 math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1009.5533,
title = {Principles of Fractional Quantum Mechanics},
author = {Nick Laskin},
journal= {arXiv preprint arXiv:1009.5533},
year = {2010}
}
Comments
31 pages