|Matrix methods are needed any course on Quantum Physics, both for
formulating and for solving problems. 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, such problems used to appear with remarkable regularity on the
physics written comprehensive exam . This is no longer relevant, since the course
is now primarily aimed at Materials, Chemistry and Nanoscience students (Quantum Physics
hasn't changed, though).
The course book, Gasiorowicz, third edition (G3, 2003), unlike some other books, does not start by using operator methods or matrices but introduces them gradually. The scattering matrix first appears in the problems for chapter 4. Operator methods are introduced in chapter 5, and used in chapter 6 to discuss the simple harmonic oscillator, whose formulation in terms of matrix operators is set out at the beginning of chapter 9. Angular momentum is discussed in chapter 7, followed by the equivalent matrix formulation in chapter 9. Then, spin, which requires a matrix treatment, is introduced in chapter 10. The corresponding chapter references for the second edition (G2, 1996) are given here.
We have followed this path very quickly, and now have to recap to solve some problems. We may also need to absorb some of the web material, previously covered in appendices in the second edition, as we go. You may do this by attempting some problems, not necessarly for credit, part revision and consolidation in preparation for the mid-term exam, where I will concentrate on conceptual problems as much as possible. The more extended problems on this material will be on problem set#3, due (after Spring Break), this year on 03/31/08. Also, at this point, it may be relevant to use my QMMS course, in particular lecture 1, since this starts with the matrix formulation.
The first search of the web that we did in 1998 under (Matrix + quantum) gave 99 entries, potentially a useful number, but I was unprepared for the mixture of doctoral theses and alternative connectedness which I found.... Most of the sites I found are now well and truly dead, but see below for some which are still there.
You could also go to the library or get out your old math books, but this is more fun. (To any member of faculty who thinks we have lost our marbles, please note that we are also doing just that..). In '98 Jennifer Trelewicz and Hu Zhan produced a nice page about linear operator/matrix methods, and Jing Tao and Hu Zhan produced a very fancy page on matrices (and tricks) which could be useful/ educational for the class (it was in the past anyway, I've taken in down now: too complicated to reinstall!)
In a lighter vein, enjoy the fruits of my surfing for matrices, using either Alta Vista ("quantum physics" + matrix)- with "matrices" and "chaos" as alternates. I had another go in 1999 with Alta Vista, and repeated the exercise several times using the excellent Google search engine:
Latest version of this document: 27th February 2008.