Spherical Harmonics In P Dimensions

Author: Costas Efthimiou
Publisher: World Scientific
ISBN: 981459671X
Size: 63.32 MB
Format: PDF
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Spherical Harmonics In P Dimensions from the Author: Costas Efthimiou. The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents:Introduction and MotivationWorking in p DimensionsOrthogonal PolynomialsSpherical Harmonics in p DimensionsSolutions to Problems Readership: Undergraduate and graduate students in mathematical physics and differential equations. Key Features:Accessible to everyone (including undergraduate students who have some knowledge in mathematics)Presents a topic that, although well-studied, is not widely disseminated in booksSolutions to all end-of-chapter problems with all the necessary details are given in the final chapter of the bookKeywords:Spherical Harmonics;Special Functions;Mathematical Physics;Green's Functions;Legendre Polynomials

The Functions Of Mathematical Physics

Author: Harry Hochstadt
Publisher: Courier Corporation
ISBN: 0486168786
Size: 51.38 MB
Format: PDF, ePub
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The Functions Of Mathematical Physics from the Author: Harry Hochstadt. Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

Mathematical Tools For Physicists

Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 3527684271
Size: 79.70 MB
Format: PDF, ePub, Mobi
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Mathematical Tools For Physicists from the Author: Michael Grinfeld. The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Mathematical Handbook For Scientists And Engineers

Author: Granino A. Korn
Publisher: Courier Corporation
ISBN: 0486320235
Size: 45.48 MB
Format: PDF, Docs
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Mathematical Handbook For Scientists And Engineers from the Author: Granino A. Korn. Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

The Theory Of Atomic Structure And Spectra

Author: Robert D. Cowan
Publisher: Univ of California Press
ISBN: 9780520906150
Size: 40.52 MB
Format: PDF, ePub, Mobi
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The Theory Of Atomic Structure And Spectra from the Author: Robert D. Cowan. Both the interpretation of atomic spectra and the application of atomic spectroscopy to current problems in astrophysics, laser physics, and thermonuclear plasmas require a thorough knowledge of the Slater-Condon theory of atomic structure and spectra. This book gathers together aspects of the theory that are widely scattered in the literature and augments them to produce a coherent set of closed-form equations suitable both for computer calculations on cases of arbitrary complexity and for hand calculations for very simple cases.

Geometry Topology And Quantum Field Theory

Author: P. Bandyopadhyay
Publisher: Springer Science & Business Media
ISBN: 9781402014147
Size: 29.70 MB
Format: PDF, Mobi
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Geometry Topology And Quantum Field Theory from the Author: P. Bandyopadhyay. This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap.