Talk:Schrödinger equation

Old discussion available at Talk:Schrödinger equation/From Talk:Schrodinger equation

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Moving to talk page per your request.

If Schrodinger is an acceptable spelling, why did you move the page to Schroedinger's equation? Everything is linked to Schrodingers equation, and nothing is linked to Schroedinger equation; we should just pick one convention and stick to it. -- CYD

(More at Talk:Schrodinger equation)

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I have a problem with the position basis material, in particular

For many (but not all) quantum systems, the state space can be spanned with a "position basis" made out of position eigenkets. For a single-particle system, we write each basis ket as |r>, which is to be interpreted as a state in which the particle is localized at position r.

Assuming that we are talking about a basis in the Hilbert space sense, and not in the Linear algebra sense, then this cannot be correct: the typical Hilbert space L²(R³) of square integrable complex functions of three variables is separable, and therefore each of its Hilbert bases is countable.

I suspect |r> is something akin to the Dirac Delta, but these are of course not elements of the Hilbert space and can therefore not constitute a basis.

It seems as if the position basis material was added in order to get from the bra-ket form of the Schrodinger equation to the wave equation. But that can be done much faster: "in many applications, the underlying Hilbert space is a space of square integrable functions, and the kets are then nothing but such functions." After all, kets are nothing but fancy notations of elements of some Hilbert space, and square integrable functions are also elements of some Hilbert space. AxelBoldt 20:50 Jan 3, 2003 (UTC)

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The first part of this page is unreadable due to superimposed PHP error messages. -- Merphant 02:11 Jan 19, 2003 (UTC)

The culprit appears to have been the following equation:

\int \left| \mathbf{r} \right> \left< \mathbf{r} \right| d^3r = \mathbf{I}

I've taken it out of the article, but now there's a gap where the equation should be, so somebody needs to fix this. It also seems to have made some of the other equations disappear. I wonder if it was just a missing math tag or something... --Camembert

Actually, it's just the equation that was immediately above the troublesome one that's disappeared (in the "The Wave Function" section). I don't know why. There's doesn't appear to be anything as obvious as a missing tag, but I don't understand the markup, so can't do anything more, really. Hopefully someone who can, will. --Camembert

Um... I think I've broken it again. Sorry. I tried to revert to Camembert's last version but it didn't seem to work... so... er... um... I'm going to go away now and hide and pretend I had nothing to do with this. -Nommo

Rather weirdly, I seem to have fixed it. The content of the page hasn't actually been changed at all, so it must have been some odd caching error. --Camembert

Idn't that the wrong equation though now? -Nommo

Oh heck. How on earth has that happened? That's not what I pasted in, I pasted in what I originally took from the article, above. Either I'm going insane, or there's gremlins in the system (the two are about equally likely, I think). --Camembert

Well, we're not getting a pageful of errors about it, but it's not rendering the equation either. In any case, I'm leaving a note on Wikipedia:TeX requests, so hopefully somebody who knows what they're doing will help. --Camembert

Ok... I've put the plain old texty version of the equation in. So there's obviously something wrong with the stuff posted up there... I guess... Works now anyway, and makes sense, and is the right equation. Just not in glorious TeXicolor. -Nommo