Quantum mechanics literature
“Not only that God does play dice, but that he sometimes confuses us by throwing them where they can’t be seen.”-Stephen Hawking
General advice
For the love of Schrodinger, do not start learning Quantum mechanics (QM) without the prerequisites. The prerequisites being at least one course in each of the following and the math needed for it - Calculus (Single and Multivariate), Vector calculus and Linear algebra:
- Classical mechanics (At least at the level of first 9 chapters of Morin)
- Electrodynamics (At least at the level of first 7 chapters of Griffiths)
- Vibrations and Waves (A student’s guide to Waves - Daniel Fleisch. The entire booklet preferably) - Wavefunction is the protagonist of QM. Do not expect understanding QM to be a smooth ride if you do not satisfy this prerequisite.
Q) Why not to skip the prerequisites?
Ans. There is a chance that you will partially understand concepts and maybe, even solve some problems in introductory texts. But, you will definitely miss a very crucial chunk of conceptual knowledge that comes by making analogies with ED. Comparing the continuity equation between ED and QM (based on the Wavefunction) can give you insights into framework of the subject better than anything else. This is only possible if you understand ED and vector calculus well already.
Q) But, What if I just want to be a “Quantum Physicist”?
Ans. There is quite a big misconception, even amongst Physics students that you can be a Quantum physicist. QM is a framework. You need this framework to explain natural phenomenon in nearly every field of physics. The extent to which you need the framework depends on the size of your domain. Whenever you are dealing with microscopic properties of a theory, you are always going to need the framework. Particle physics, AMO physics (atomic and molecular physics), condensed matter physics, Quantum computing & information, Biophysics are the fields where you have to use this framework at each and every step as your domain of interest is tiny particles. In Condensed matter and Biophysics you deal with ensembles of particles, where you use Statistical mechanics (Classical or Quantum depending on the scenario) in abundance.
Q) (Keen eye observer) You didn’t mention Astrophysics? Is it because we are dealing with big/heavier objects?
Ans. Exactly. For most of the situations where you are dealing with macroscopic bodies, heavy in mass, you would use General relativity for precise calculations. But, many times you might want to look into the microscopic properties responsible for these macroscopic bodies. A good example that comes to mind is stability of Stars. (Naively speaking) The gravitational pull of the stars should make them collapse into themselves, but they don’t for a significant phase of their lifetime. This is due to something called as the degeneracy pressure which can only be explained using QM.
Introductory Books
There are a LOT of introduction to QM books out there. These ones according to me are the ones with the highest impact/page ratio. My top recommendation would be the lecture notes by Barton Zweibach for 8.04,8.05 (8.06 will be considered in the Adv.QM literature post) - see below in Video lectures.
Introduction to Quantum Mechanics - David.J.Griffiths
The holy grail of all books for beginners in Quantum mechanics. He is reading a story to you. Chapter 1 and 2 are dedicated to the very basic yet extremely important concepts of QM. Solve most of the problems in these chapters to make a concrete foundation. The book is divided into two parts (in any logical course, you will do one part in a single semester course). The second part of the book can get fairly advanced at times. It definitely covers almost everything that one would need before transitioning to QFT.(Someone who has read the Electrodynamics literature, might have realized it is the same advice. Yeah, both the books do jobs very parallel fashion - which makes sense as they are by the same author)
A Modern Approach to Quantum Mechanics - Townsend
He mentions in his preface that he uses Feynman’s and Sakurai’s books as his primary motivation. Although, the goal of both the books is drastically different, they are excellent individually. Feynman’s books caters to the very beginner in QM and Sakurai’s book is literally a graduate level text focusing heavily on advanced topics that eventually would help one transition to Quantum field theory (QFT) in general or Condensed matter physics or Atomic and molecular physics. Townsend’s book does a brilliant job in finding the middle ground. He also covers path integrals which are the bread-and-butter of QFT. I personally enjoyed reading this book after I had a decent knowledge of QM already. But, I can easily see it being used as an introductory text.Principles of Quamtum mechanics - Rammaruti Shankar
This fat, hardbound (usually) red book covers everything you need in QM. From the basics of linear algebra needed to Born approximation needed to transition to QFT, he covers every single topic (Including path integrals). Why is this in beginner books? It’s the best reference out there for any topic you need.A student’s guide to Schrodinger’s equation - Daniel Fleisch
This 150 page booklet is in no manner a substitution to a proper text like Griffiths. But, it does a wonderful job in summarizing the most important results. This is an excellent resource to get an gist of what you will be learning.
Advanced reference books
- Modern Quantum Mechanics - J.J. Sakurai
I already talked about the purpose of this book while talking about Townsend. Its a relatively advanced book but in no way a book for the beginner. I personally love this book due to the fact that even after being catered towards a Physics audience, he keeps the mathematical precision very tight. As mentioned before, probably one of the best books to help one transition from QM to QFT. (MIT’s 806 is the next strong contender ) - Course in Theoretical Physics III : Quantum mechanics (Non relativitic theory) - Landau Lifsitz
Honorable mentions
- Quantum mechanics - Gasiorowicz
- Quantum mechanics - Auletta, Fortunato, Parisi
- Quantum mechanics - Florian Scheck
- Quantum mechanics - Auletta, Fortunato, Parisi
- Quantum mechanics - Daniel Bes
- Quantum mechanics - Basdevant, Dalibard
Freely available online sources
Video lectures / MOOCs
MIT : There are no better courses than these for QM (on the Internet and on the planet). The problem sets are not for the faint hearted. No matter for what purpose you are learning QM, I highly recommend reading the first 14 chapters of 8.04 from the OCW link. These chapters are essentially crucial for foundational purposes.
- QM a first course : 8.04 MIT edX, OCW
- Mastering QM : 8.05 MIT edX, OCW
- Applications of QM : 8.06 MIT edX, OCW
Lecture notes - Generally complement well in parallel to a formal course
