Fractional quantum mechanics is a recently developed natural generalization of quantum mechanics. This book summarizes fundamentals and applications of fractional quantum mechanics. The book presents the fractional Schrö dinger equation, which is a manifestation of fractional quantum mechanics. A new theoretical tool — fractional path integral — the path integral over Lévy flights, has been presented. The fractional path integral method enhances the well-known Feynman path integral framework. The book covers related topics on time fractional quantum mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is helpful as a monograph and a handbook for theorists, pure and applied mathematicians, solid-state physicists and chemists working with the Schrö dinger equation, the path integral technique and applications of fractional calculus in different research areas. Key Features: ○ This is the first monograph on fractional quantum mechanics — a recently emerged and fast growing field of quantum theory ○ It extends applications of fractional calculus to quantum theory ○ It has been written by the founder of fractional quantum mechanics ○ It presents recently developed fundamentals on the fractional Schrö dinger equation and fractional path integral, and their applications to quantum mechanics and quantum statistical mechanics ○ A new theoretical physics tool — the fractional path integral, presented for the first time by the book, significantly enhances the well-known Feynman’s path integral approach to quantum mechanics and statistical physics ○ Never before used in quantum mechanics, the Fox H-function and the Mittag-Leffler function have been introduced and used to obtain close form solutions of fractional quantum mechanical problems

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