|Eigenvalue problems form an important part of any course on Quantum
Physics. Since this is a one-semester course with (at least in part) a
review character, we can't spend nearly as much time on this topic as we
would do in a two or three semester course sequence. Nonetheless, as I'm
sure you are aware, such problems appear with remarkable regularity on
the comprehensive exam...
The main course book, Gasiorowicz, third edition (G3, 2003), spends chapters 3 and 4 on this topic, and there is much that is useful there, and in the second edition - we just can't do all of it explicitly. However, I will grade any problems you do from these books, and we might like to add some comments to particular aspects or problems which can be linked to this page. For reference the topics in the books are classified in the outline below. I have added some section and page number references to an alternate course book, Liboff, fourth edition (L4, 2003). The corresponding page references for Gasiorowicz's 2nd edition (G2, 1996) and Liboff's 3rd edition (L3, 1998) are given here.
Separation of variables (G3 p44-47, and/or L4, section 3.4, p80-84)
This 1D example is used to demonstrate the expansion postulate and
There is an enormous amount of material here. I'd suggest a background read, questions in class, and then a concerted attack on a few problems which interest you. Some of these are on Problem set #2. Then we can share our questions and experience at a later date.
Latest version of this document: 30th January 2008.