Talk:Particle in a box

Thanks! A nice, detailed article.

Maybe we should mention that we are using the time-independent Schrödinger equation here, which is different from the one on Schrodinger wave equation. Or maybe that page should be changed.

Also, is it a coincidence that all ψ_n are real-valued functions? Shouldn't complex numbers show up? --AxelBoldt

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Thanks for the compliment on the article. I just added a statement that we are using the time-independent Schroödinger equation. I think it would be useful to add this equation to the Schrodinger wave equation page and explain when its use is appropriate (probably a task for someone more knowledgeable on this subject than myself).

As for the absense of complex numbers, my understanding is that complex numbers, indicate the "phase" of the system and arise in the time-dependent equation. Since the particle in a box is a time-independent problem and corresponds to a standing wave there is no time-dependent portion and hence no complex component to the solution. If anyone more knowledgeable than myself on this subject can confirm or deny this explanation, I would greatly appreciate it.--Matt Stoker

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About the doubt above: the wavefunctions for time-independent quantum mechanics problems ARE complex in general, and not necessarily real. The example in this article is simple and compelling because they are real, but in general they can be complex. A simple example of a complex standing wave are the electron states in a hidrogen atom. - Ernesto.

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In this case, the wavefunctions are real because the problem is one-dimensional. Generically, one-dimensional solutions to the S. wave equation have no phase variation, so we might as well take them to be real. -- CYD

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The math markup on this article is ghastly. The hbar looks horrible, the fractions are done using (num)/(den) which also looks horrible when it is done everywhere, and the integral limits look horrible as well. I would like to Tex-ify this article when I have time, or someone else can do it, unless there is large protest against it. --dave

As for: I would like to Tex-ify this article

The (fortunately!) few instances of TeX-urication in Wikipedia seem to make the fonts of their articles ghastly inconsistent, both in size and in type.

I've seen this complaint before, but I don't really buy it. The fonts for the formulas are bigger than the text, but the formulas are all the same size. So I don't really see any "inconsistency". The font size of the formulas are just bigger than the text, which makes them stand out. It's no big deal if the formula stands out. For the tex-math stuff inline, this can screw up the spacing between lines, but but only for certain math things. Just simple greek symbols don't cause any problem.

As for: The hbar looks horrible

How does one set one's Wikipedia:Preferences for how HTML operators (such as "<strike>") are implemented and rendered? And: why might this article require any particular "struck-out unit" anyways?

Best regards, Frank W ~@) R 20:34 Apr 2, 2003 (UTC)

I'm not sure if I understand you, but the "struck-out" unit is necessary in this case to adhear to convention. It is h-bar which is a standard unit in quantum mechanics. It prevents having to write out 2*Pi everywhere. --dave

Ok, about the above stuff....I think tex for the indented formulas is great. Much better than the html. But tex is definitely bad for inline stuff. But I think using html in the inline stuff is ok, and yes that makes the font size inconsistent of variables with the main formula, but it's okay, it's still the same letters and it can still be italic, so I don't see this as a huge factor. At least, I think having the main formula in TeX looks so much nicer that it outweighs any concern for the font sizes being inconsistent. --dave

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Does anyone know why formula in 18 and 19 the square root sign is slanted in one, but not the other? Thanks. --dave

pure speculaion from my part: it's because 'y' is slighty longer than 'x'; if you replace:

<math>Y_{n_y}=\sqrt{\frac{2}{L_y} \sin \left( \frac{n_y \pi y}{L_y} \right) } \quad (19)</math>

by

<math>Y_{n_y}=\sqrt{\frac{2}{L_y} \sin \left( \frac{n_y \pi y}{L_x} \right) } \quad (19)</math>

^

|

then both are slanted! -- looxix 20:30 Apr 3, 2003 (UTC)

Thanks looxix, I tried fixing it using \vphantom{y} but it doesn't support that command for some reason.... --dave

So it's solved now (was my fault sorry). -- looxix 00:11 Apr 4, 2003 (UTC)

Oh, you mean because the root sign shouldn't have been over the sine? I thought I was the one that did that... oh well --dave