Solving WKB Eigenvalue Problem for Bound States

[T-7]

Hi,

This is just a quick question -- I'm puzzled by the way this answer sheet represents the potential function.

The question asks us to determine the energy eigenvalues of the bound states of a well where the potential drops abruptly from zero to a depth Vo at x=0, and then increases linearly with position x until at x=a the potential is again zero.

They write:

$$V(x) = \frac{V_{0}x}{a}$$
$$E = V(b) = \frac{V_{0}b}{a}$$

where b is some point between x=0 and x=a.

But surely the correct representation of the potential function is

$$V(x) = V_{0}\left(\frac{x}{a}-1\right)$$

so that V(0) = -Vo, and V(a) = 0. But, using my potential function, I end up with a somewhat different expression for the energy eigenvalues, in the end, than they do. Why do they do it that way? And what's wrong with my pot. function??

Cheers!

 

[Gokul43201]

There's nothing wrong with your function; if your description of the problem is a faithful reproduction (which is why we prefer if the original question is reproduced verbatim, rather than paraphrased) then "they" got it wrong.

 

[T-7]

There's nothing wrong with your function; if your description of the problem is a faithful reproduction (which is why we prefer if the original question is reproduced verbatim, rather than paraphrased) then "they" got it wrong.

Ok. Thanks for confirming that.