Hilbert spaces in QM


by dextercioby
Tags: hilbert, spaces
dextercioby
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#1
Jan23-04, 04:30 AM
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...For abut two weeks i've searching the internet for a good online (i.e.free for download)course on the basis of quantum mechanics,that means the mathematical background of this theory.I found a few,especially from American colleges,but all of them seemed to have serious problems regarding mathematical and logcal coherence.I mean all of them do not make the distinction between hermitic and self adjoint operators(and it's obviously not all).
I find this distinction to be of some relevance in quantum mechanics,don't you?
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selfAdjoint
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Jan23-04, 09:57 AM
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Originally posted by dextercioby
...For abut two weeks i've searching the internet for a good online (i.e.free for download)course on the basis of quantum mechanics,that means the mathematical background of this theory.I found a few,especially from American colleges,but all of them seemed to have serious problems regarding mathematical and logcal coherence.I mean all of them do not make the distinction between hermitic and self adjoint operators(and it's obviously not all).
I find this distinction to be of some relevance in quantum mechanics,don't you?
Yes and no. It's Hermitian, BTW. The difference is not noticable in the stuff you do in introductory QM and most intro courses don't want to swamp the students in fancy dan Hilbert space / C*-algebra / functional analysis stuff, that requires almost a full unit in itself to get really up to speed. I'd say go with the flow, keeping in mind that there is a difference and it will be time enough for you to bring your knowledge of that to bear after you are skilled with the basics.
vacuum
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#3
Jan26-04, 08:57 AM
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Heh, unfortunately, there are some places on the Earth that do not wish to follow the mainstream. Students of physics in Belgrade
do have the pleasure to meet Hilbert spaces in all their complexity in a super-condensed one semestre crash course at undergrad level.
I know that this faculty(www.ff.bg.ac.yu) has some courses already translated in English, so you could give it a try. They, definitely have an online pdf text on Hilbert spaces, however it is in Serbian. ;-)


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