Responsible party: East End, Devlin

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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.

Steps to the Analytic Method:

1) Use dimensionless form of DE

<math>let \xi = \sqr [(m\omegax}/\hbar)] </math> and <math> K=(2E)/(\hbar\omega). </math>

Then we can use the dimensionless form of the Schrodinger <math> \frac{\partial^2}{\partial x^2}=(\xi^2-K)\psi(x) </math>

We can think of <math> \xi </math> as approximately <math> x </math> and also <math> \psi </math> as approximately <math> e^(-(\xi)^2/2)</math>.

2.) <math> \psi~h(\xi)e^(-\xi/2) </math> <math> \frac{\partial^2}{\partial x^2}=(\xi^2-K)\psi(x) </math>

3.) Substitute <math> \psi </math> into <math> \frac{\partial^2}{\partial x^2}=(\xi^2-K)\psi(x). </math>

Then, <math> \frac{\partial^2h(\xi)}{\partial \xi^2}=-2\xih(\xi)+(K-1)(h(\xi)=0 </math>

4>) Use power series to come up with an expression

{2m}\frac{\partial^2}{\partial x^2}+\frac{1}{2} k \strike{\omega} x^2. </math>

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