Fractional Calculus: An Introduction For Physicists (Third Edition)
World Scientific, 09.07.2018 - 636 Seiten
'The third edition of this book is designed to carefully and coherently introduce fractional calculus to physicists, by applying the ideas to two distinct applications: classical problems and multi-particle quantum problems. There remain many open questions and the field remains an active area of research. Dr Herrmann’s book is an excellent introduction to this field of study.'Contemporary PhysicsThe book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute in the development of this exciting research area.This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory.Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.
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18 qDeformed Lie Algebras and Fractional Calculus
19 Infrared Spectroscopy of Diatomic Molecules
20 Fractional Spectroscopy of Hadrons
21 Magic Numbers in Atomic Nuclei
22 Magic Numbers in Metal Clusters
23 Towards a Geometric Interpretation of Generalized Fractional Integrals
24 Fractors Fractional Tensor Calculus
25 Fractional Fields
9 Fractional Calculus in Multidimensional Space 2DImage Processing
10 Fractional Calculus in Multidimensional Space 3DFolded Potentials in Cluster Physics A Comparison of Yukawa and Coulomb Potentials with Ri...
11 Quantum Mechanics
12 The Fractional Schrödinger Equation with Infinite Well Potential Numerical Results Using the Riesz Derivative
13 Uniqueness of a Fractional Derivative The Riesz and Regularized Liouville Derivative as Examples
14 Fractional Spin A Property of Particles Described with the Fractional Schrödinger Equation
17 The Fractional Symmetric Rigid Rotor
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Abramowitz and Stegun analytic apply behavior Caputo derivative classical consequence coordinate corresponding cos(ka covariant defined derivative operator described determined differential equation dimensional Dirac eigenfunctions eigenvalue spectrum eigenvalues energy levels experimental exponential field fission frac fractal fractional calculus fractional derivative fractional derivative definition fractional extension fractional harmonic oscillator fractional integral fractional rotation group fractional Schrödinger equation fractional symmetric rigid fractional wave equation geometric given Greiner Herrmann intentionally left blank interpreted kinetic energy Lagrangian density linear Liouville magic numbers mass meson Mittag-Leffler function nonlocal nonlocalization operator nuclear nuclei obtain parameter parity particle Phys physics plotted polynomials problems properties quantum harmonic oscillator quantum mechanics quark Riesz derivative rigid rotor rotation group sin(ka ſº solutions space spectra spherical standard symmetric rigid rotor tensor term theory Thick lines tional values vibrational wave equation