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Topics in Quantum Mechanics (Progress in Mathematical Physics)

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Topics in Quantum Mechanics

Progress in Mathematical Physics

By Floyd Williams

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Format: Hardcover, 398 pages, 2003 Edition
Other Information: Illustrated
Published In: United States, 23 January 2003
The theories of quantum fields and strings have had a fruitful impact on certain exciting developments in mathematics and have sparked mathematicians' interest in further understanding some of the basic elements of these grand physical theories. This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov--Uvarov theory of generalized hypergeometric differential equations to solve the Schrvdinger equation and to obtain the quantization of energies from a single unified point of view. This theory is developed and is also used to give a uniform approach to the theory of special functions. Additional key features: * Considerable material is devoted to the foundations of classical mechanics using conventional mathematical terminology * The first 10 chapters of Part I cover Planck and Schrvdinger quantization, Pauli's spin functions, and an introduction to multielectron atoms * Part II treats such topics as Feynman path integrals, quantum statistical partition functions, high and low temperature asymptotics of quantum fields of over a negatively curved space-time * Selected special topics involve some applications of the theory of automorphic forms, zeta functions, the Jacobi inversion formula, spherical harmonic analysis and the Selberg trace formula * Excellent bibliography and index. Communication between physicists and mathematicians requires continual bridges to eliminate the divide. This monograph furthers that goal in presenting some new and exciting applications ofso-called pure mathematics, including number theory, to various problems arising in physics. An excellent resource for classroom or self-study.

Table of Contents

Preface * Part I. Introductory Concepts in Quantum Theory * Units of Measurement * Quantum Mechanics---Some Remarks and Themes * Equations of Motion in Classical Mechanics * Quantization and the Schrodinger Equation * Hypergeometric Equations and Special Functions * Hydrogen-like Atoms * Heisenberg's Uncertainty Principle * Group Representations and Selection Rules * A Charged Particle in an Electro-magnetic Field * Spin Wave Functions * Introduction to Multi-electron Atoms * Part II. Some Selected Topics * Fresnel Integrals and Feynman Integrals * Path Integral for the Harmonic Oscillator * Euclidean Path Integrals * The Density Matrix and Partition Function * Zeta Regularization * Helmholtz Free Energy and the Selberg Trace Formula * The Zeta Function of a Product * Two Guest Lectures * Some Further Electron Configurations * Mendeleev Periodic Table * Another Example of Zeta Regularization * Integral Evaluation * Some Informal Comments on QFT * References * Index

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Reviews

"... a number of interesting and classical applications (some involving detailed computations) are included. Most of the book is dedicated to covering the traditional material but there are also some innovations, both in the choice of topics and in the way they are presented... overall, I shall say that this is a very good text that is welcome both from the conceptual and the operational points of view. The theoretical physics community should also find here a good source on the subject." --Mathematical Reviews

EAN: 9780817643119
ISBN: 0817643117
Publisher: Birkhauser
Dimensions: 24.18 x 16.36 x 2.39 centimetres (0.69 kg)
Age Range: 15+ years
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