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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!
...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!