For all you Math / QM freaks out there.... ....check out this paper: F. Gieres, Rep. Prog. Phys. 63 (2000), pp. 1893 - 1931, "Mathematical surprises and Dirac's formalism in quantum mechanics" which you can find here: http://www.iop.org/EJ/abstract/0034-4885/63/12/201 (requires subscription) You can download the paper for FREE here: http://arxiv.org/abs/quant-ph/9907069 (English) or http://arxiv.org/abs/quant-ph/9907070 (French). The author shows that the lack of a rigorous mathematical formalism in QM leads to contradictions that are quite interesting. He illustrates problems and also gives solutions to them how to avoid them. Have fun!