Basic Physics(12th level):
- Mathematical Methods in the Physical Sciences, Mary L. Boas. Not my favorite but will do the job. Also, starts off at a rudimentary level so everyone might find it useful.
- Mathematical Methods for Physicists, by Arfken, Weber and Harris. This book is comprehensive and has pretty much everything you need with enough problems to keep you busy. I found it especially useful for Complex Analysis, Special Functions and Integral transforms. It is a intermediate level book so I wouldn’t recommend starting with this first.
- Linear Algebra, Hoffman and Kunze. This is my favorite when it comes to linear algebra. It has amazing problems and a very rigorous development of the subject all the way from basic linear transforms to spectral decomposition(also covers matrices and determinants better than most others I know). Although I have listed this as a post grad level book, doing this earlier will help you understand Quantum Physics a lot better. If this feels like too much maths, then go for Gilbert Strang.
- Complex Analysis, Lars V. Ahlfors. This is your complete guide to a mathematically rigorous treatment of complex numbers.
- Classical Mechanics, Herbert Goldstein. Has been the standard reference across the world for many decades now.
- An Introduction to Mechanics, Daniel Kleppner and Robert Kolenkow. Another classic, more accessible than Goldstein at an undergraduate level.
- Mechanics, L. D. Landau and E. M. Lifshitz. Terse if used by itself but has some unique observations which can be very helpful.
- Introduction to Electrodynamics, D. J. Griffiths. Elementary and informal treatment. One of the best books available for your first venture into Maxwell’s theory.
- Classical Electrodynamics, J. D. Jackson. Probably the most respected and most feared of the standard references of all time. Can’t escape this at graduate level.
- Classical Electricity and Magnetism, Wolfgang K. H. Panofsky and Melba Philips. Another classic which I found easier to read than Jackson.
- Classical Electrodynamics, Julian Schwinger et al. Really good book but I hate it for personal reasons.
- The Feynman Lectures on Physics, Vol. II. This one is very much recommended to get a understanding of the physical aspect of the subject in real life examples.
Thermodynamics and Statistical Physics:
- Fundamentals of Thermal and Statistical Physics, Frederick Reif. Not universally loved but will do the job. Builds up the subject nicely starting from probability itself.
- Concepts in Thermal Physics, Stephen J. Blundell and Katherine M. Blundell. A very informal treatment of the subject, useful for undergraduates.
- Statistical Mechanics, R. K. Pathria and Paul D. Beale. Standard reference at graduate level. As good a reference as any but I found the development a bit boring.
- Introduction to Statistical Physics, Huang Kerson.
- Thermodynamics and an Introduction to Thermostatistics, Herbert B. Callen. I liked the way this book handles the Maths involved.
There’s Landau and Lifshitz volume 5 and volume 9 too but I haven’t personally read them. Just for fun, you can check out an older work “Elements of classical thermodynamics” by A. B. Pippard, it is quite a unique treatment of the topic.
- Introduction to Quantum Mechanics, D. J. Griffiths. Just like the ED book, this is a elementary and informal treatment of the subject. Best book out there as an introduction to the subject.
- Modern Quantum Mechanics, J. J. Sakurai and Jim Napolitano. Standard reference, good problems, comprehensive treatment.
- Quantum Mechanics, Volumes I and II, Claude Cohen-Tannoudji, Bernard Diu and Frank Laloe. No treatment of the subject gets any more comprehensive than this. Pretty much all there is to know about non-relativistic Quantum Mechanics.
- Principles of Quantum Mechanics, Paul Dirac. From the master himself, the book is not an easy read and one can get lost in all the mathematics of representations at first. It is quite interesting once you get the hang of it. Very rigorous treatment.
- An Introduction to Quantum Mechanics: A Time-Dependent Perspective, David J Tannor. Not a standard reference in Physics as it is directed mainly towards Quantum Chemistry but I found it very useful to understand QM at work with density functional approach and especially loved the way it explains the Bohmian perspective using a hydrodynamic formulation of non-relativistic QM.
- The Feynman Lectures on Physics, Vol. III. As always, nothing beats Feynman in seeing the physics in all that maths.
Solid State Physics:
- Solid State Physics, Ashcroft and Mermin. Heavy in the mathematics and dense in information, one of my favorites since undergrad. Indian teachers for some reason avoid this and stick to easier books.
- Introduction to Solid State Physics, Charles Kittel. Teachers’ favorite and very accessible.
- Solid State Physics, A. J. Dekker. Standard stuff, easier than Ashcroft.
- Introduction to Special Relativity, Robert Resnick. Short and intuitive development and good problems to illustrate the concepts rather than just doing algebra with the formulae.
- Special Relativity and Classical Particle Dynamics, R. D. Sard. Good book to bridge the gap between understanding relativity as a concept and actually putting it to use in problems.
- Relativistic Kinematics, R. Hagedorn. Book by a CERN scientist that teaches you to apply relativity to collision problems.
- Introductory Nuclear Physics, Kenneth S Krane.
- Introduction to Elementary Particles, D. J. Griffiths.
If you want more specific recommendations for any advanced topic in maths, QM or GR, email me at [email protected]