Wavevector in infinite square well

[Master J]

Right guys, I want to get this one straight...

We have all seen the simple infinite square well a million times. From it, we can get the condition for the k-vector of the electron that

k = n.pi / L

Now, I also come across all the time that k = 2n.pi / L

When do we use which boundary condition? They both seem to come from the same situation, but I cannot see when one is used?

It's a simple situation that's been bugging me a while! Hope someone can clear this up.

Cheers!

 

[Matterwave]

The wave-function needs to disappear at the 2 boundaries, so whichever k produces the disappearing wave-function at the 2 boundaries is the k that you should use. Usually the problem is defined so that L is the total length of the square well, so you should use the first one. The second one would be used if the total length of the square well was, for some reason, 1/2L.

 

[jtbell]

It would help if you could give us specific references to sites/books/whatever that do it each way, otherwise we have to guess.

My guess is that it's because some sources define the well as having width L, with either 0 < x < L or -L/2 < x < +L/2; and some define the well as having width 2L, with -L < x < L.

 

[Matterwave]

Did I get the lengths backwards...? Should it be L and 2L? My apologies if I did, I just tried to work it out in my head.

 

[Master J]

I can't actually think of any right now, I just know I've seen it come up. For instance, in deriving the Density of States from the Free Electron Model.

So you think it's just from the fact that one can define the width of the well as L or 2L?