Hyperspherical Harmonics And Their Physical Applications
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Hyperspherical Harmonics And Their Physical Applications
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Author : James Emil Avery
language : en
Publisher: World Scientific
Release Date : 2017-11-27
Hyperspherical Harmonics And Their Physical Applications written by James Emil Avery and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Science categories.
Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use.
Hyperspherical Harmonics
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Author : John S. Avery
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hyperspherical Harmonics written by John S. Avery and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
where d 3 3)2 ( L x - -- i3x j3x j i i>j Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3-dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a d-dimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (3-27»: The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A , chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3-dimensional space. Similarly, one finds that a d-dimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations ( 4 - 27) and ( 4 - 30) ) : 00 ik·x e = (d-4)!!A~oiA(d+2A-2)j~(kr)C~(~k'~) 00 (d-2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O ). l). l)J where I(O) is the total solid angle. This expansion of a d-dimensional plane wave is useful when we wish to calculate Fourier transforms in a d-dimensional space.
An Elementary Treatise On Spherical Harmonics And Subjects Connected With Them
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Author : Norman Macleod Ferrers
language : en
Publisher:
Release Date : 1877
An Elementary Treatise On Spherical Harmonics And Subjects Connected With Them written by Norman Macleod Ferrers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1877 with Spherical harmonics categories.
Introduction To Modern Methods Of Quantum Many Body Theory And Their Applications
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Author : Adelchi Fabrocini
language : en
Publisher: World Scientific
Release Date : 2002-08-19
Introduction To Modern Methods Of Quantum Many Body Theory And Their Applications written by Adelchi Fabrocini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-19 with Science categories.
This invaluable book contains pedagogical articles on the dominant nonstochastic methods of microscopic many-body theories — the methods of density functional theory, coupled cluster theory, and correlated basis functions — in their widest sense. Other articles introduce students to applications of these methods in front-line research, such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics that are of current relevance. The book addresses the striking lack of pedagogical reference literature in the field that allows researchers to acquire the requisite physical insight and technical skills. It should, therefore, provide useful reference material for a broad range of theoretical physicists in condensed-matter and nuclear theory.
State Of The Art Of Molecular Electronic Structure Computations Correlation Methods Basis Sets And More
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Author :
language : en
Publisher: Academic Press
Release Date : 2019-09-07
State Of The Art Of Molecular Electronic Structure Computations Correlation Methods Basis Sets And More written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-07 with Science categories.
State of the Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More, Volume 79 in the Advances in Quantum Chemistry series, presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology. Chapters in this new release include Computing accurate molecular properties in real space using multiresolution analysis, Self-consistent electron-nucleus cusp correction for molecular orbitals, Correlated methods for computational spectroscopy, Potential energy curves for the NaH molecule and its cation with the cock space coupled cluster method, and much more. - Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology - Features detailed reviews written by leading international researchers
The De Sitter Ds Group And Its Representations
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Author : Mohammad Enayati
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
The De Sitter Ds Group And Its Representations written by Mohammad Enayati and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Science categories.
This book reviews the construction of elementary systems living in de Sitter (dS) spacetime, in both the classical and quantum senses. Field theories on dS spacetime are among the most studied mathematical models of the Universe, whether for its earlier period (inflationary phase) or for its current phase of expansion acceleration (dark energy or cosmological constant). Classical elementary systems are Hamiltonian phase spaces, which are associated with co-adjoint orbits of the relativity group. On the other hand, quantum elementary systems are associated with (projective) unitary irreducible representations of the (possibly extended) relativity group (or one of its covering). This study emphasizes the conceptual issues arising in the formulation of such systems and discusses known results in a mathematically rigorous way. Particular attention is paid to: “smooth” transition from classical to quantum theory; physical content under vanishing curvature, from the point of view of a local (“tangent”) Minkowskian observer; and thermal interpretation (on the quantum level), in the sense of the Gibbons-Hawking temperature. Such a mathematical construction is of paramount importance to the understanding of the early Universe (due to the critical role that the dS metric plays in the inflationary cosmological scenarii) as well as to the construction of possible models for late-time cosmology (since a small positive cosmological constant or dark energy seems to be required by recent data). In this sense, this book uniquely blends mathematical physics (spacetime symmetry on classical and quantum levels) and theoretical physics (quantization, quantum field theory, and cosmology). Moreover, the level of exposition varies in different parts of the book so that both experts and beginners alike can utilize the book.
Phonation
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Author : Ephraim Cutter
language : en
Publisher:
Release Date : 1895
Phonation written by Ephraim Cutter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1895 with Architectural acoustics categories.
Register Of The University Of California
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Author : University of California, Berkeley
language : en
Publisher:
Release Date : 1894
Register Of The University Of California written by University of California, Berkeley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1894 with categories.
Tables Of Angular Spheroidal Wave Functions
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Author : United States. Naval Research Office
language : en
Publisher:
Release Date : 1975
Tables Of Angular Spheroidal Wave Functions written by United States. Naval Research Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Tables Of Angular Spheroidal Wave Functions Prolate M
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Author : Naval Research Laboratory (U.S.)
language : en
Publisher:
Release Date : 1975
Tables Of Angular Spheroidal Wave Functions Prolate M written by Naval Research Laboratory (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Spheroidal functions categories.