This recommendation assumes that a text at the level of Arfken or Butkov has been completed as an undergraduate.
- Principles of Advanced Mathematical Physics Volumes I & II by Robert Richtmyer
- Mechanics by Landau & Lifshitz is a good place to start. Brilliant exposition, but too short; this can serve as a supplement to the standard Goldstein text.
- Classical Mechanics (3rd Edition) by Herbert Goldstein et al
- Theoretical Mechanics of Particles and Continua by Fetter & Walecka. The first half (on particles) is standard, the material is the same as (but the exposition inferior to) Goldstein or L&L. The second part (on continua) provides excellent coverage of a great deal of material that is not covered in ANY of the other standard graduate mechanics texts.
- Problems and Solutions on Mechanics: Major American Universities Ph.D. Qualifying Questions and Solutions by Yung-Kuo Lim
- Classical Electrodynamics by John David Jackson
- Electrodynamics of Continuous Media by Landau & Lifshitz
- Problems and Solutions on Electromagnetism (Major American Universities Ph.D. Qualifying Questions and Solutions) and Problems and Solutions on Optics (Major American Universities Ph.D. Qualifying Questions and Solutions) by Yung-Kuo Lim
- Unfortunately, undergraduate quantum mechanics does not adequately prepare you for the material you'll have to tackle in graduate quantum mechanics. Invariably there are (sometimes amazingly large) gaps which must be filled in before moving on. Two outstanding texts for doing this are Quantum Mechanics (3rd Edition) by Leonard Schiff and Quantum Mechanics: Non-Relativistic Theory, Third Edition by Landau & Lifshitz
- Once that's accomplished, you can move on to "relativistic quantum mechanics" and quantum field theory. The standard treatment is in Relativistic Quantum Mechanics and Relativistic Quantum Fields by Bjorken & Drell, which is a bit dated but still quite valuable. A much more accessible (and consequently less thorough) treatment can be found in Relativistic Quantum Mechanics: Wave Equations, Quantum Electrodynamics and Field Quantization by Walter Greiner.
- Quantum Electrodynamics by Landau & Lifshitz contains material not covered in either of the treatments mentioned in the previous bullet point, in particular with respect to phenomenology and calculational techniques.
- Quantum Field Theory by Itzykson & Zuber rounds out and brings up to the date the material in the previously mentioned books.
- Problems and Solutions on Quantum Mechanics: Major American Universities Ph. D. Qualifying Questions and Solutions (Major American Universities Ph. D. Qualifying Questions and Solutions) and Problems and Solutions on Atomic, Nuclear and Particle Physics: Major American Universities Ph.D. Qualifying Questions and Solutions by Yung-Kuo Lim, just to prove you know what you're talking about.
Statistical Mechanics:
- Statistical Mechanics by Donald McQuarrie
- Statistical Mechanics: A Set of Lectures by Richard Feynman
- Statistical Physics and Physical Kinetics by Landau & Lifshitz
- Problems and Solutions on Thermodynamics and Statistical Mechanics (Major American Universities Ph.D. Qualifying Questions and Solutions) by Yung-Kuo Lim
General Relativity:
I'm not sure why so few graduate programs include general relativity. It's really hard to consider yourself a fully educated physicist without having a grounding in this subject.
- Gravitation by Misner, Thorne & Wheeler for unparalleled breadth
- General Relativity by Robert Wald for added depth in the more important parts and a more modern treatment than MTW
- The Classical Theory of Fields by Landau & Lifshitz. This book has several very good chapters on electrodynamics, but it is for its discussion of relativity that you should devour this book.
- Problems and Solutions on Relativity and Miscellaneous Topics (Major American Universities Ph. D. Qualifying Questions and Solutions) by Yung-Kuo Lim
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