Responsible party: poit0009, Pluto 4ever

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Please try to include the following

• main points understood, and expand them - what is your understanding of what the points were.
  • expand these points by including many of the details the class discussed.
• main points which are not clear. - describe what you have understood and what the remain questions surrounding the point(s).
  • Other classmates can step in and clarify the points, and expand them.
• How the main points fit with the big picture of QM. Or what is not clear about how today's points fit in in a big picture.
• wonderful tricks which were used in the lecture.

We discussed the discussion problem from yesterday (Oct 6). We have the potential:

<math>V(x)= -\alpha[\delta(x-a)+\delta(x+a)] </math>

We can separate <math>\psi(x)</math> into three regions:

<math>\psi_1(x)</math>, where x < -a

<math>\psi_2(x)</math>, where -a < x < a

<math>\psi_3(x)</math>, where x > a

The wave functions end up being:

<math>\psi_1(x)=Ae^{(kx)}</math>

<math>\psi_2(x)=Be^{(kx)}+Ce^{(-kx)}</math>

<math>\psi_3(x)=De^{(-kx)}</math>

with <math>k^2=-\frac{2mE}{\hbar^2}</math>

We end up getting:

<math>{\small^+_-} e^{-2ak}=2bk-1</math>, where <math>b=\frac{\hbar^2}{2m\alpha}</math>

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