1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to find the wave function using WKB?

  1. Dec 15, 2013 #1
    I would like to understand how to find wave functions using WKB.

    1. The problem statement, all variables and given/known data

    Given an electron, say, in the nuclear potential

    $$U(r)=\begin{cases}
    & -U_{0} \;\;\;\;\;\;\text{ if } r < r_{0} \\
    & k/r \;\;\;\;\;\;\;\;\text{ if } r > r_{0}
    \end{cases}$$

    With the barrier region given by:

    $$r_{0} < r < k/E$$

    What is the wave function inside the barrier region?

    2. Relevant equations

    See below.

    3. The attempt at a solution

    For E > U(r):

    $$\psi(r)=\frac{Ae^{i\phi(x)}}{\sqrt{2m(E-U(r)}}+\frac{Be^{-\phi(x)}}{\sqrt{2m(E-U(r)}}$$

    $$\phi(r)=\frac{1}{\hbar}\int^{r}_{0}\sqrt{2m(E-U(r')}=\frac{1}{\hbar}\int^{r}_{0}\sqrt{2m(E+U_{0})}dr'=\frac{r\sqrt{2m(E+U_{0})}}{\hbar}$$

    Is the above integral correct? Is that simply all that I needed to do?
     
    Last edited: Dec 15, 2013
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: How to find the wave function using WKB?
  1. Orbital Wave Functions (Replies: 0)

Loading...