This is a question, not an answer, but: Has anyone here read [Singer's "Linearity, symmetry and prediction in the hydrogen atom"][1]? I'm a sucker for a good example, and it seems like this could be a good grounding for the daunting task of understanding quantum mechanics. [1]: http://books.google.com/books?id=Brme1xhBjoYC&printsec=frontcover&dq=Linearity,+Symmetry,+and+Prediction+in+the+Hydrogen+Atom&ei=lWDzSsu5NpWWygTjv83EDQ#v=onepage&q=&f=false