Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman
This book (based off of these lectures) came out a few years ago, and while I picked it up at launch I never quite finished it and it got kind of lost on the back burner. The third book on special relativity just came out, though, so I dusted this one off and finally completed it. Recall that this quantum mechanics volume is the second in Susskind’s Theoretical Minimum series, after the first book on classical mechanics.
A few years ago at my old university we had David Griffiths as an invited guest speaker. I didn’t take notes so I could be misremembering, but I recall him saying that while the physics education profession had more or less decided on the appropriate structure for a course on electromagnetism, there was still widespread disagreement about how to teach quantum mechanics. Griffiths’ own book starts with the Schrodinger equation on page one, and proceeds from simple potentials like the infinite square well up through the hydrogen atom and beyond, and then moves on to other topics like spin. Longair’s Quantum Concepts in Physics instead takes an historical approach.
Susskind and Friedman take a different tack: they start with spin, which doesn’t really have any classical analogue and hence is rather foreign and abstract. However, the mathematics of spin is comparatively very simple (on the order of 2×2 matrices). I’m not sure of this approach. Having take several quantum mechanics courses, it was all fairly old hat to me, but I’m not sure that a beginner wouldn’t feel a bit overwhelmed right off the start. The advantage of beginning with spin is that they are very well placed to then explore issues like entanglement (Chapters 6 and 7). They do a very thorough job developing and motivating the algebra of operators, and having started with spin there’s always ready-made and simple examples to apply the operators to.
While they never solve the infinite square well or the hydrogen atom, the last chapter is devoted to the harmonic oscillator. It’s not as thoroughly developed as in a textbook like Griffiths, since it starts off by declaring but not proving a theorem that the ground state has no nodes, and then the ground state wave function is just given to us. However, they then develop the raising and lowering operators to generate the higher-energy wave functions, whose solutions involve the Hermite polynomials.
In his video lecture series, Susskind had a second course on advanced quantum mechanics, and so I wonder if they’ll eventually publish a similar book in this series. Before that though there’s the third book on special relativity, then presumably we’ll get general relativity, cosmology, and statistical mechanics.