Overview

Such theories as quantum fields and strings have had a fruitful impact on certain developments in mathematics and have the sparked the interests of mathematicians towards a further understanding of some of the basic elements of these physical theories. This monograph navigates through the basic elements of quantum mechanics for a readership of mathematical researchers and graduate students whose background in physics might be rather modest. It should also be of interest to students and researchers in physics. Features include: topics such as Feynman path integrals, quantum statistical partition functions, high and low temperature asymptotics of quantum fields over a negatively curved space-time; a systematic application of the Nikiforov-Uvarov theory of generalised hypergeometric differential equations to solve the Schrodinger equation and to obtain the quantization of energies from a single elegant point of view; application of zeta functions, the Jacobi inversion formula, spherical harmonic analysis and the Selberg trade formula.

Full Product Details

Author:   Floyd Williams
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2003 ed.
Volume:   27
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.787kg
ISBN:  

9780817643119

ISBN 10:   0817643117
Pages:   398
Publication Date:   23 January 2003
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

I Introductory Concepts in Quantum Theory.- 0 Units of Measurement.- 1 Quantum Mechanics: Some Remarks and Themes.- 2 Equations of Motion in Classical Mechanics.- 3 Quantization and the Schrödinger Equation.- 4 Hypergeometric Equations and Special Functions.- 5 Hydrogen-like Atoms.- 6 Heisenberg’s Uncertainty Principle.- 7 Group Representations and Selection Rules.- 8 The Quantized Hamiltonian for a Charged Particle in an Electromagnetic Field.- 9 Spin Wave Functions.- 10 Introduction to Multi-Electron Atoms.- II Some Selected Topics.- 11 Fresnel Integrals and Feynman Integrals.- 12 Path Integral for the Harmonic Oscillator.- 13 Euclidean Path Integrals.- 14 The Density Matrix and Partition Function in Quantum Statistical Mechanics.- 15 Zeta Regularization.- 16 Helmholtz Free Energy for Certain Negatively Curved Space-Times, and the Selberg Trace Formula.- 17 The Zeta Function of a Product of Laplace Operators and the Multiplicative Anomaly for X?d.- 18 Schrödinger’s Equation and Gauge Theory.- About the Author.- General Appendices.- Appendix A: Some Further Electron Configurations.- Appendix B: Mendeléev Periodic Table.- Appendix C: Determinants for String World-Sheets That Are Tori: Another Example of Zeta Regularization.- Appendix E: Some Informal Comments on QFT.- References.

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. <p>a Mathematical Reviews

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