# 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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### Inhalt

 1 Introduction 1 2 Functions 7 3 The Fractional Derivative 37 4 Friction Forces 55 5 Fractional Calculus 65 6 The Fractional Harmonic Oscillator 91 7 Wave Equations and Parity 99 8 Nonlocality and Memory Effects 109
 18 qDeformed Lie Algebras and Fractional Calculus 277 19 Infrared Spectroscopy of Diatomic Molecules 291 20 Fractional Spectroscopy of Hadrons 311 21 Magic Numbers in Atomic Nuclei 337 22 Magic Numbers in Metal Clusters 373 23 Towards a Geometric Interpretation of Generalized Fractional Integrals 387 24 Fractors Fractional Tensor Calculus 417 25 Fractional Fields 421

 9 Fractional Calculus in Multidimensional Space 2DImage Processing 129 10 Fractional Calculus in Multidimensional Space 3DFolded Potentials in Cluster Physics A Comparison of Yukawa and Coulomb Potentials with Ri... 143 11 Quantum Mechanics 163 12 The Fractional Schrödinger Equation with Infinite Well Potential Numerical Results Using the Riesz Derivative 189 13 Uniqueness of a Fractional Derivative The Riesz and Regularized Liouville Derivative as Examples 201 14 Fractional Spin A Property of Particles Described with the Fractional Schrödinger Equation 221 15 Factorization 227 16 Symmetries 245 17 The Fractional Symmetric Rigid Rotor 255
 26 Gauge Invariance in Fractional Field Theories 433 The One Dimensional Case 443 28 On the Origin of Space 491 29 Outlook 507 Appendix A Solutions to Exercises 509 Bibliography 557 Index 603 Urheberrecht