Topics in Quantum Mechanics / by Floyd Williams.
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 mechani...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boston, MA :
Birkhäuser Boston,
2003.
|
| Series: | Progress in mathematical physics ;
27. |
| Subjects: |
MARC
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| 100 | 1 | |a Williams, Floyd. | |
| 245 | 1 | 0 | |a Topics in Quantum Mechanics / |c by Floyd Williams. |
| 260 | |a Boston, MA : |b Birkhäuser Boston, |c 2003. | ||
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| 490 | 1 | |a Progress in Mathematical Physics ; |v 27. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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 Schr"dinger 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 Schr"dinger 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 of so-called pure mathematics, including number theory, to various problems arising in. | ||
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| 830 | 0 | |a Progress in mathematical physics ; |v 27. | |
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