Do wavefunctions in 1D potential wells have n maxima at energy level En?

[Lisa...]

Is it true that, no matter what, the number of tops the wave functions of the energy levels in a one dimensional potential well (like the one shown below) have is the same as the number of that energy level? I.e. does in every well the wavefunction have 1 top in E1, 2 in E2, 3 in E3 etc?

 

[Allday]

Hi Lisa,

for a potential well it is true in general that the probability distributions for the eigenfunctions will have n anti-nodes where n is the quantum number that labels the states as well as the energies. I think this is what you mean by 'tops', as they will all be maxima. ie n = 1 has one maximum, n=2 has two and so forth.

ps i didn't look at the picture. either the link is broken or the computer I am on won't let me see it

gabe

 

[Lisa...]

Hey there!

Thanks a bunch for your quick reply! It feels good to know I finally begin to understand a bit of these potential wells... And btw: I'm terribly sorry 'bout the picture! I already thought something went wrong... Oh well here's it again if you want to see it:

Lisa

Ps Yeah I did mean maxima of the sine I just couldn't come up with the correct English word for it fast :D In the Netherlands we call them 'toppen' (that's why I wrote tops) or 'buiken' (which literally means bellies). Of course the word maxima is used too, but not quite often. Perhaps it has something to do with the (crown)prinses from Argentina whose name is Maxima...

 

[Lisa...]

If the image still does not work try:

http://img360.imageshack.us/img360/5966/potentialwell3cv.th.gif