Fractional Calculus: An Introduction for PhysicistsWorld Scientific, 2011 - 261 Seiten Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in the subjects of classical mechanics, friction, damping, oscillations, group theory, quantum mechanics, nuclear physics, and hadron spectroscopy up to quantum field theory. |
Inhalt
1 Introduction | 1 |
2 Functions | 5 |
3 The Fractional Derivative | 11 |
4 Friction Forces | 23 |
5 Fractional Calculus | 33 |
6 The Fractional Harmonic Oscillator | 57 |
7 Wave Equations and Parity | 65 |
8 Nonlocality and Memory Effects | 75 |
13 The Fractional Symmetric Rigid Rotor | 133 |
14 qdeformed Lie Algebras and Fractional Calculus | 153 |
15 Fractional Spectroscopy of Hadrons | 165 |
16 Higher Dimensional Fractional Rotation Groups | 187 |
Fractional Tensor Calculus | 219 |
18 Fractional Fields | 223 |
19 Gauge Invariance in Fractional Field Theories | 231 |
20 Outlook | 241 |
9 Quantum Mechanics | 93 |
a Property of Particles Described with the Fractional Schr ̈odinger Equation | 111 |
11 Factorization | 117 |
12 Symmetries | 123 |
Bibliography | 243 |
| 257 | |
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Häufige Begriffe und Wortgruppen
analytic angular momentum ansatz apply baryon behaviour Caputo derivative Caputo fractional derivative Casimir operators charmonium classical coefficient consequence coordinate corresponding derivative operator described determined dh w(a eigenfunctions eigenvalues energy levels extended Fourier frac fractional calculus fractional derivative fractional derivative according fractional derivative definition fractional extension fractional fields fractional friction fractional harmonic oscillator fractional integral fractional rotation group fractional Schrödinger equation fractional symmetric rigid fractional wave equation free fractional Schrödinger gauge field geometric given ground state band harmonic oscillator interaction interpreted Lagrangian density leads level spectrum Lie algebras linear Liouville magic numbers meson metal clusters Mittag-Leffler function nonlocal nuclei obtain particle Phys physics potential properties proposed q-number quantum mechanics quark Riemann fractional derivative rotation group shell correction shell model sin(a sin(kx solutions space spectra spherical standard symmetric rigid rotor symmetric rotor theory tional valid values vibrational wave equation