I am currently struggling to understand my basic introductory course on quantum statistical mechanics and I have done a basic course on single particle quantum mechanics.
I was wondering whether anyone knows of any good resources (online/books) that I could read to help my understanding of this subject.
I would like to read about the following topics : quantum microcanonical ensemble, quantum canonical ensemble, quantum grand canonical ensemble, quantum harmonic oscillators, ideal quantum gases, spin and statistics and many particle states.
Answer
There are of course many books out there, quantum statistics is a really well-established field, so regardless of suggestions here you should really look further on your own as well and find one that suits you best. But here are a few that I've used in the past that you may find useful:
Statistical mechanics: A survival guide by Mike Glazer and Justin Wark. It's a book based on the lectures notes given by the two authors, so the material does not go into the advanced topics too much and sticks with minimum necessary basics. After 3 nice chapters on classical stat. mech. mainly discussing distinguishable particles, it moves over to indistinguishable particles and first develops the classical version then introduces the concept of Gibbs paradox, with this transitions toward quantum statistics for the remaining part of the book. Einstein statistics, quantum dist. functions, photon gas etc. Bear in mind it may not contain all that you're looking for, but it is a good start and very easy to read.
Landau & Lifshitz Vol. 5 is of course always recommended, and you have it also online for free. Big part of the book is dedicated to classical stat. mech. but starting from chapter 5 it moves over to the quantum version, a lot of in-depth discussions, but does also cover some simple examples of photon gas or lin. harmonic oscillator.
One that comes closest to the specific topics you mentioned is Statistical mechanics A set of Lectures by Richard P. Feynman. Note it is not part of the 3-volume Feynman lectures, it's another book solely on stat. mech. based on Feynman's lecture notes. It's really a modern book, in the sense that it is mainly focused on quantum statistics and adopts the more common notations of Dirac's bra-ket, traces etc. Basically all the calculations are shown in this book (pages and pages of it), no real steps omitted. Chapter 1 and 2 are of main interest to you: Discussing the partition function for a system of discrete E states, LHO, Q-statistics for many particle systems, then chapter two is really a priceless in-depth discussion of density matrices and their use in stat. mech., after a long intro (covering some QM basics as well) it starts discussing specific examples such LHO, 1D free particle all using density matrices (more advanced topics come next).
Anyway again, there are many books, impossible to tell which one is best for you, but here's another one: Introduction to Modern Statistical Mechanics David Chandler. One of my favorites, it's one of those books that does tell all the tricks and intuitive ideas that other books skip out on. You can start from any chapter and still be able to read through while understanding most of it. The chapter 4 starts discussing non-interacting systems by re-discussing the occupation number in quantum stats, photon gases etc. Then moves over to ideal gases of real particles discussing the grand canonical potential for bosons and fermions.
Finally if you want to go for some of thick well known (covering almost everything, mainly for references (not many calcs shown)), then here are two that I recommend: Statistical Mechanics 3rd edition by Pathria (chapter 5 to 9 cover all the topics you mention), and Statistical Mechanics by McQuarrie with a nice first chapter reminding everything on thermodynamics, QM etc. This book first discusses quantum statistics and only few chapter later returns to classical stat mech (briefly) (chapter 4,6 and 10 discuss most elements of Q-statistics.)
Please take the time to check out the table of contents of all the books mentioned, read the reviews, see excerpts of the books on google books.
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