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This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.
In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Contents:- Introduction
- Hamiltonian Mechanics
- Mathematical Foundations of Quantum Mechanics
- Dirac's Ket- and Bra-Formalism
- Schrödinger Equation and Liouville Equation
- Quantum Mechanics of the Harmonic Oscillator
- Green's Functions
- Time-Independent Perturbation Theory
- The Density Matrix and Polarization Phenomena
- Quantum Theory: The General Formalism
- The Coulomb Interaction
- Quantum Mechanical Tunneling
- Linear Potentials
- Classical Limit and WKB Method
- Power Potentials
- Screened Coulomb Potentials
- Periodic Potentials
- Anharmonic Oscillator Potentials
- Singular Potentials
- Large Order Behavior of Perturbation Expansions
- The Path Integral Formalism
- Classical Field Configurations
- Path Integrals and Instantons
- Path Integrals and Bounces on a Line
- Periodic Classical Configurations
- Path Integrals and Periodic Classical Configurations
- Quantization of Systems with Constraints
- The Quantum-Classical Crossover as Phase Transition
- Summarizing Remarks
Readership: Undergraduates and graduate students in physics; researchers in mathematical and particle physics.
- Sales Rank: #1951363 in eBooks
- Published on: 2012-07-19
- Released on: 2012-07-19
- Format: Kindle eBook
Review
"The unique aspect of this book is that is uses parallel application of both the Schrödinger equation and path integral to few selected problems with enough details. Useful references from original literatures are added at the end of the book. This book can be used as reference book for advanced graduate-level courses in quantum physics. This book may also be useful for researchers working in quantum physics." -- Contemporary Physics
Reviews of the First Edition:
"... for all readers interested in specific aspects of perturbation methods, path integrals, and their applications in classical field theory, this book provides a valuable source for their studies." -- Mathematical Reviews
"It will be useful for theoretical physicists who wish to enlarge their skill in quantum mechanics and for postgraduate students studying quantum mechanics on a deep level." -- Zentralblatt MATH
From the Inside Flap
This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schr dinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behaviour of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.
In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.
Most helpful customer reviews
4 of 4 people found the following review helpful.
A solid and detailed book on QM
By Rudi Podgornik
Great exposition of QM, conceptually and formally. After the Electrodynamics, this is the second book of Harald J. W. Muller-Kirsten that I read. Both are quite technical and include all the relevant calculational details. Also they contain materials that is usually not available in other books. Also the part on path integral formulation is well done and could be used as a separate course material on purely path integral approach to QM.
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