Quantum Mechanics references
TL;DR: I recommend reading chapter 1 of John S. Townsend.1 And then skim through Hitoshi Murayama;2 Daniel F. Styer et al.3 Lucien Hardy4 in that order to see if you find anything useful there. The rest are good references if you want to search for a topic.
Physics textbooks / lecture notes
- David J. Griffiths and Darrell F. Schroeter5
-
a standard textbook on QM at the undergraduate level.
- Townsend6
-
another textbook on QM at the undergraduate level. The difference with Griffiths and Schroeter7 is how it “bootstrap” QM, i.e. what physical system is used to first introduce the subject. The latter starts with wave function and then dive right into how probability density is related to that. The problem of this approach is it immediately starts with many complicated mathematical concepts as the space is continuous—square-integrable space, probability density, etc. The former bootstrap by starting with the simplest possible non-trivial Hilbert space of dimension 2: spin \(\frac{1}{2}\) system. I.e. it starts with finite dimensional Hilbert spaces and focuses on the foundational concepts of QM in relation to Hilbert space, before generalizing it to the continuous cases. This all makes sense if you think how statistics should be introduced from discrete random variables before moving on to continuous case which involve much more mathematical subtlety.
- J. J. Sakurai and Jim Napolitano8
-
a standard textbook on QM at the graduate level.
- Steven Weinberg9
-
a graduate textbook on QM by the Nobel Laureate Steven Weinberg. This is a good reference, but don’t expect this to be a light read.
- Murayama10
-
a graduate level lecture note by a very good teacher, prof. Murayama, on the topic of quantum statistics. It is a gentle introduction on why quantum statistics is the way it is (i.e. why spin implies two different kinds of quantum statistics behavior). It however requires basic understanding of QM so it may not be a good first read as an introduction. Other lecture notes under the same URL are at similar level and usefulness: http://hitoshi.berkeley.edu/221B/.
For mathematicians / theoretical physicists
- Brian C. Hall11
-
introduces QM at graduate level mathematics. It bridges the gap where the mathematically heavy subject, quantum mechanics, is often presented in a not-so-mathematical way. It intermixes both the physical ideas and the mathematical foundation behind the subject. To quote the author:
The twin goals of the book are (1) to explain the physical ideas of quantum mechanics in language mathematicians will be comfortable with, and (2) to develop the necessary mathematical tools to treat those ideas in a rigorous fashion.
- Hardy12
-
an interesting axiomatic approach to quantum theory. 5 axioms are presented, where the first 4 is compatible with “classical probability theory”. I.e. the last axiom leads to quantum theory, providing an insight on what quantum theory is. This provides a more abstract, philosophical background of what QM is, which is often interesting to mathematicians but not so much for a typical physicist. This can be a light read by skimming through the gist of the mathematical ideas behind it.
- Styer et al.13
-
another interesting read about the foundation of QM. It outlines 9 different TFAE (The Followings Are Equivalent) ways to formulate QM. It includes for example matrix, wave function, density matrix approaches which is commonly used in QM, and path integral formulation commonly used in QFT (Quantum Field Theory). It can be useful as physicists often use these approaches (especially the first 3) interchangeably which can be confusing to an outsider.
References
Footnotes
A Modern Approach to Quantum Mechanics, 2. ed (University Science Books, 2012).↩︎
“Many-Body Problems I (Quantum Statistics),” February 28, 2005, http://hitoshi.berkeley.edu/221B/statistics.pdf.↩︎
“Nine Formulations of Quantum Mechanics,” American Journal of Physics 70, no. 3 (2002): 288–97, https://doi.org/10.1119/1.1445404.↩︎
“Quantum Theory From Five Reasonable Axioms,” arXiv:quant-ph/0101012, preprint, arXiv, September 25, 2001, https://doi.org/10.48550/arXiv.quant-ph/0101012.↩︎
Introduction to Quantum Mechanics, 3rd ed. (Cambridge University Press, 2018), https://doi.org/10.1017/9781316995433.↩︎
Modern Quantum Mechanics, 2nd ed. (Cambridge University Press, 2017), https://doi.org/10.1017/9781108499996.↩︎
Lectures on Quantum Mechanics, 2nd ed. (Cambridge University Press, 2015), https://doi.org/10.1017/CBO9781316276105.↩︎
Quantum Theory for Mathematicians, vol. 267, Graduate Texts in Mathematics (Springer New York, 2013), https://doi.org/10.1007/978-1-4614-7116-5.↩︎