Hyperspherical Harmonics Expansion Techniques
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Hyperspherical Harmonics Expansion Techniques
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Author : Tapan Kumar Das
language : en
Publisher: Springer
Release Date : 2015-11-26
Hyperspherical Harmonics Expansion Techniques written by Tapan Kumar Das and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Science categories.
The book provides a generalized theoretical technique for solving the fewbody Schrödinger equation. Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles. The introduction of Jacobi vectors, hyperspherical variables and hyperspherical harmonics as an expansion basis is an elegant way to tackle systematically the problem of an increasing number of interacting particles. Analytic expressions for hyperspherical harmonics, appropriate symmetrisation of the wave function under exchange of identical particles and calculation of matrix elements of the interaction have been presented. Applications of this technique to various problems of physics have been discussed. In spite of straight forward generalization of the mathematical tools for increasing number of particles, the method becomes computationally difficult for more than a few particles. Hence various approximation methods have also been discussed. Chapters on the potential harmonics and its application to Bose-Einstein condensates (BEC) have been included to tackle dilute system of a large number of particles. A chapter on special numerical algorithms has also been provided. This monograph is a reference material for theoretical research in the few-body problems for research workers starting from advanced graduate level students to senior scientists.
Hyperspherical Harmonics And Their Physical Applications
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Author : James Emil Avery
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
Hyperspherical Harmonics And Their Physical Applications written by James Emil Avery and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 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.
The Augmented Spherical Wave Method
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Author : Volker Eyert
language : en
Publisher: Springer
Release Date : 2007-06-26
The Augmented Spherical Wave Method written by Volker Eyert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-26 with Science categories.
The Augmented Spherical Wave (ASW) method is one of the powerful approaches to handle the requirement of finite basis sets in DFT calculations. It is particularly suited for the calculation of elastic properties and phonon spectra of solid-state materials. This book addresses all those who want to learn about methods for electronic structure calculations and the ASW method in particular.
Stochastic Variational Approach To Quantum Mechanical Few Body Problems
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Author : Yasuyuki Suzuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01
Stochastic Variational Approach To Quantum Mechanical Few Body Problems written by Yasuyuki Suzuki 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 2003-07-01 with Science categories.
The quantum-mechanical few-body problem is of fundamental importance for all branches of microphysics and it has substantially broadened with the advent of modern computers. This book gives a simple, unified recipe to obtain precise solutions to virtually any few-body bound-state problem and presents its application to various problems in atomic, molecular, nuclear, subnuclear and solid state physics. The main ingredients of the methodology are a wave-function expansion in terms of correlated Gaussians and an optimization of the variational trial function by stochastic sampling. The book is written for physicists and, especially, for graduate students interested in quantum few-body physics.
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.
Innovative Computational Methods In Nuclear Many Body Problems Towards A New Generation Of Physics In Finite Quantum Systems
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Author : Hisashi Horiuchi
language : en
Publisher: World Scientific
Release Date : 1998-09-02
Innovative Computational Methods In Nuclear Many Body Problems Towards A New Generation Of Physics In Finite Quantum Systems written by Hisashi Horiuchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-02 with categories.
The recent rapid innovations in supercomputer technology are changing the concepts of numerical calculations employed in solving a wide variety of nuclear many-body problems. The purpose of the XVII RCNP International Symposium on Innovative Computational Methods in Nuclear Many-Body Problems (INNOCOM97) was to discuss the frontiers of various computational methods and to exchange ideas in wide fields of nuclear physics. The subjects discussed at the symposium covered almost all the areas of nuclear physics.
Numerical Methods For Wave Equations In Geophysical Fluid Dynamics
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Author : Dale R. Durran
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Numerical Methods For Wave Equations In Geophysical Fluid Dynamics written by Dale R. Durran 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 2013-03-14 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIlas the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in AppliedMathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and en courage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the AppliedMathematical Sei ences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface This book is designed to serve as a textbook for graduate students or advanced undergraduates studying numerical methods for the solution of partial differen tial equations goveming wave-like flows. Although the majority of the schemes presented in this text were introduced ineither the applied-rnathematics or atmos pheric-science literature, the focus is not on the nuts-and-bolts details of various atmospheric models but on fundamental numerical methods that have applications in a wide range of scientific and engineering disciplines.
Biological Effects And Health Implications Of Radiofrequency Radiation
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Author : James C. Lin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Biological Effects And Health Implications Of Radiofrequency Radiation written by James C. Lin 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 2013-03-09 with Technology & Engineering categories.
The study of electromagnetic bioeffects is multidisciplinary; it draws heavily from the disciplines of physics, engineering, mathematics, biol ogy, chemistry, medicine, and environmental health. This book is about these disciplines and how they mutually integrate in the study of electromagnetic pathophysiology. Over aperiod of years, the authors have become increasingly aware of the difficulty in locating information concerning interaction of electro magnetic energy and biological tissues. There are numerous reports and publications, but no single comprehensive source in the American literature where such information is readily accessible. Regrettably, much of the importantinformation is contained in government documents and reports, some of which are inaccessible, or spread through many diverse journals, making retrieval and analysis of the material difficult. Although this book is primarily clinically oriented, it also focuses on those biophysical, biochemical, and fundamental molecular studies and findings that provide the basis for understanding the presence or absence of pathophysiological manifestations of exposure to radiofrequency, including microwave, energies. Detailed discussion and analysis of the relevant comprehensive physics, engineering, and biophysics are con tained in Chapters 2-5. Because the treatment is multidisciplinary, wherever possible analy sis is begun with basic background information that may appear elementary to some readers but is essential to understanding for those from a different discipline. Most confusion and controversies that exist in the field today arise from individuals of one discipline not appreciating basic facts or theories from another.
Micromechanics Of Heterogeneous Materials
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Author : Valeriy Buryachenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-20
Micromechanics Of Heterogeneous Materials written by Valeriy Buryachenko 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 2007-09-20 with Science categories.
Here is an accurate and timely account of micromechanics, which spans materials science, mechanical engineering, applied mathematics, technical physics, geophysics, and biology. The book features rigorous and unified theoretical methods of applied mathematics and statistical physics in the material science of microheterogeneous media. Uniquely, it offers a useful demonstration of the systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature.
Mathematical Methods For Physics And Engineering
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Author : Mattias Blennow
language : en
Publisher: CRC Press
Release Date : 2018-01-03
Mathematical Methods For Physics And Engineering written by Mattias Blennow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-03 with Science categories.
Suitable for advanced undergraduate and graduate students, this new textbook contains an introduction to the mathematical concepts used in physics and engineering. The entire book is unique in that it draws upon applications from physics, rather than mathematical examples, to ensure students are fully equipped with the tools they need. This approach prepares the reader for advanced topics, such as quantum mechanics and general relativity, while offering examples, problems, and insights into classical physics. The book is also distinctive in the coverage it devotes to modelling, and to oft-neglected topics such as Green's functions.