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Mathematical Concepts of Quantum Mechanics
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.
Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content.
It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group.
With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.
Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content.
It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group.
With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.
382 pages, Paperback
First published July 28, 2003
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Displaying 1 - 2 of 2 reviews
May 28, 2018
Partial reading on chapter 1-5 and 9.14. I was mainly interested in basic notion and quick introduction to bounded operators, self-adjoint operators, unitarity, spectral mapping, trace class operators, etc and less so on actual quantum mechanics of scattering states etc. It turned out useful for those chapters, because it got me into what I wanted pretty quickly and less daunting than swallowing a graduate text in mathematics (which may be useful if I have time and need dedication for it). May revisit again one day.
March 12, 2025
i’ve read the first 10 chapters + chapter 25,26 of this and im counting it. Will have read first 17-20 by end of sem.
Pros:
- readable
- mostly interesting
- lends itself as a good reference text with some explanations
cons
- no solutions to selected problems.
Overall, this book (or a book like this) is a must read after Griffiths. Definitely gives good insights to the role of functional analysis in QM.
Pros:
- readable
- mostly interesting
- lends itself as a good reference text with some explanations
cons
- no solutions to selected problems.
Overall, this book (or a book like this) is a must read after Griffiths. Definitely gives good insights to the role of functional analysis in QM.
Displaying 1 - 2 of 2 reviews