Good books on the group theory of quantum mechanics

In summary, the conversation is about finding good books on group theory in quantum mechanics. The individual has a background in physics and electrical engineering, with experience in laser systems. Their goal is to study and understand quantum electrodynamics. Some book recommendations are given, including Greiner & Müller's Quantum Mechanics: Symmetries and S. Sternberg's Group Theory and Physics. Other suggestions include Ballentine's Quantum Mechanics and Weinberg's Lectures on Quantum Mechanics for the Galilei group, and Weinberg's The Quantum Theory of Fields for the relativistic case. A more general book on symmetry in physics is also mentioned. The individual thanks the group for their suggestions.
  • #1
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Hello
I'm looking for good books on the group theory of quantum mechanics. I have a BS in Physics, MS in Electrical Engineering and decades of work experience in building lasers, and R&D in laser systems, optics & infrared sensing systems.

My main goal is to study & understand quantum electrodynamics.

Thanks
 
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  • #3
I like S. Sternberg's "Group Theory and Physics". In contrast to the authors of most other books on group theory as applied to physics, he isn't a physicist but a mathematician. This has the effect that the presentation of the methods is much more modern and up to date than what can be found in other books. For example, it is the only book where I found a comprehensible explanation of the uses of Young diagrams in physics.
 
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  • #4
A good treatment of the Galilei group in quantum theory can be found in Ballentine, Quantum Mechanics and Weinberg, Lectures on Quantum Mechanis. For the relativistic case I recommend Weinberg, The quantum theory of fields.

A more introductory book, not restricted to quantum theory but more general about (Poincare) symmetry in physics is Relativity, Groups, Particles.
 
  • #5
Thanks folks, I'll look into these suggestions.

PS: I have Weinberg, The quantum theory of fields Volume 1. I've read the first 80 pages three times- and then I'm lost.
 

1. What is the best book for beginners to learn about group theory in quantum mechanics?

The most highly recommended book for beginners is "Group Theory in Quantum Mechanics" by Volker Heine. It provides a clear and concise introduction to the subject, with plenty of examples and exercises to enhance understanding.

2. Are there any textbooks on group theory in quantum mechanics that are suitable for self-study?

Yes, "Group Theory and its Application to the Quantum Mechanics of Atomic Spectra" by Eugene P. Wigner is a great option for self-study. It includes detailed explanations and a variety of problems to help readers grasp the concepts.

3. Which book covers both group theory and its applications in quantum mechanics?

"Symmetry and the Standard Model: Mathematics and Particle Physics" by Matthew Robinson is a comprehensive book that covers both group theory and its applications in quantum mechanics. It is suitable for both beginners and advanced readers.

4. Are there any books that focus specifically on the application of group theory in quantum chemistry?

"Group Theory and Chemistry" by David M. Bishop is a highly recommended book for those interested in the application of group theory in quantum chemistry. It covers the fundamentals of group theory and its applications in molecular structure and bonding.

5. Can you recommend a book that discusses the latest advancements in group theory in quantum mechanics?

"Group Theory in Quantum Mechanics: An Introduction to its Present Usage" by Marcelo R. Ubriaco is a comprehensive book that covers the latest advancements in group theory in quantum mechanics. It is suitable for graduate students and researchers in the field.

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