The more I read volume III of the Feynman Lectures on Physics about Quantum Mechanics the better I like it. Even having taken two courses in it 60 and 10 years ago, Feynman takes a completely different tack, plunging directly into what makes quantum mechanics different than anything else.
He starts by saying “Traditionally, all courses in quantum mechanics have begun in the same way, retracing the path followed in the historical development of the subject. One first learns a great deal about classical mechanics so that he will be able to understand how to solve the Schrodinger equation. Then he spends a long time working out various solutions. Only after a detailed study of this equation does he get to the advanced subject of the electron’s spin.”
Not to worry, he gets to the Hamiltonian on p. 85 and the Schrodinger equation p. 224. But he is blunt about it “We do not intend to have you think we have derived the Schrodinger equation but only wish to show you one way of thinking abut it. When Schrodinger first wrote it down, he gave a kind of derivation based on some heuristic arguments and some brilliant intuitive guesses. Some of the arguments he used were even false, but that does not matter. “
When he gives the law correct of physics for a particle moving freely in space with no forces, no disturbances (basically the Hamiltonian), he says “Where did we get that from” Nowhere. It’s not possible to derive it from anything you know. It came out of the mind of Schrodinger, invented in his struggle to find an understanding of the experimental observations of the real world.” How can you not love a book written like this?
Among the gems are the way the conservation laws of physics arise in a very deep sense from symmetry (although he doesn’t mention Noether’s name). He shows that atoms radiate photons because of entropy (p. 69).
Then there is his blazing honesty “when philosophical ideas associated with science are dragged into another field, they are usually completely distorted.”
He spends a lot of time on the Stern Gerlach experiment and its various modifications and how they put you face to face with the bizarrities of quantum mechanics.
He doesn’t shy away from dealing with ‘spooky action at a distance’ although he calls it the Einstein Podolsky Rosen paradox. He shows why if you accept the way quantum mechanics works, it isn’t a paradox at all (this takes a lot of convincing).
He ends up with “Do you think that it is not a paradox, but that it is still very peculiar? On that we can all agree. It is what makes physics fascinating”
There are tons more but I hope this whets your appetite
Chemiotics II 