2017/03/28 by Nick Laskin · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #Fractional Differential Equations Solutions #Quantum Information and Cryptography #Advanced Mathematical Theories and Applications #Path integral formulation #Quantum statistical mechanics #Statistical mechanics #Mathematics #Quantum mechanics #Fractional Brownian motion #Quantum dissipation #Physics #Classical mechanics #Quantum #Brownian motion
paper · doi:10.1142/10541
openalex publication_date 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
"Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches."--Publisher's website