User talk:24.155.72.152

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If you looking for the above IP address on a math page, it's probably me. Mct mht 06:29, 4 April 2006 (UTC)

[edit] preview button

Would be good if you use the preview button a bit, as many saves mess up the history. Thanks. Oleg Alexandrov (talk) 00:27, 2 April 2006 (UTC)

[edit] please do not delete people's comments

Do not delete people s comment's on talk pages please. Moreover, your comment is wrong. The bra-ket space is a space which includes position and momentum "eigenstates", which do not live in L²(R). However, even if the comment were wrong, it's not appropriate to delete. -lethe ^{talk +} 09:12, 2 April 2006 (UTC)

No such thing as states which does not belong to a Hilbert space, this is a misconception shared by some in the physics community. You belong to that group. Your notion of eigenvectors and spectrum is mathematically incorrect. Such misconceptions lead to language like, for example, "eigenstates of the position operator" are the dirac delta functions, which obviously not in L^2. Or the "eigenfunctions" of the momentum operator, which has unit modulus all at values, which again are not in L^2. Actually both the position operator and momentum operator have no discrete spectrum. —This unsigned comment was added by mct_mht (talk • contribs) .

These notions can be rigorously defined in a rigged Hilbert space. It's a common arrogance among mathematicians to assume that just because a mathematician hasn't defined something, then it's nonsense. In fact, many definitions in mathematics are made after physicists start using them. -lethe ^{talk +} 09:36, 2 April 2006 (UTC)

Incorrect is incorrect. No point throwing terms like "rigged Hilbert spaces" about when one doesn't even know what spectrum means. In fact, rigged Hilbert spaces are arguably too sophiticated a fix for the present discussion. —This unsigned comment was added by mct_mht (talk • contribs) .

Uh, well it is true that rigged Hilbert spaces are more complicated with little pay-off. Nevertheless, they do provide a framework within which many unbounded operators have eigenvalues. When you say incorrectly that "they don't exist mathematically", you really just mean "they don't exist in the most common mathematical framework of Hilbert space". Once again, I want to say: just because mathematicians don't use rigged Hilbert space, does not mean that physicists are incorrect to do so. Luckily I know what a spectrum is, so I don't have to feel bad about throwing around other terms, too. -lethe ^{talk +} 09:45, 2 April 2006 (UTC)

If you're familiar with the requisite notions of functional analysis, please accept my apologies. Obviously one can't talk about rigged Hilbert spaces competently without it, otherwise one is reduced to the same level some physics texts discusses "Hilbert spaces," only difference is that the objects now looks superficially more sophisticated. In good ol Hilbert spaces, there's a perfectly fine formulation of measurement that uses spectral measures and resolution of the identity. Arguably the only advantange of a rigged space, if that's what it is, is that notion of eigenvectors and eigenvalues now survives the passage to the rigorous. —This unsigned comment was added by mct_mht (talk • contribs) .

You're right about this. The sole reason for introducting rigged Hilbert spaces is to make the physicist's usage rigorous, and spectral theory is more successful in Hilbert space, and so rigged Hilbert spaces don't really do much. One thing they do do is make mathematicians wrong who like to go around claiming that physicists are doing nonsense or wrong mathematics when they do quantum mechanics. -lethe ^{talk +} 21:05, 2 April 2006 (UTC)

Ha! Maybe I was wrong about rigged spaces being a completely waste of time. Maybe. The paper quant-ph/0603177 on arXiv might be of interest. Mct mht 23:36, 4 April 2006 (UTC)

[edit] Question

How about making an account, and also using an edit summary, so that people understand what you are doing with each edit? Both would be really helpful to us,your fellow wikipedians. Cheers, Oleg Alexandrov (talk) 19:05, 2 April 2006 (UTC)

Ok, good advice. —This unsigned comment was added by mct_mht (talk • contribs) .

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