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classes:2009:fall:phys4101.001:lec_notes_0925

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Sept 25 (Fri) SHO: Analytical method

Responsible party: East End, Devlin

To go back to the lecture note list, click lec_notes
previous lecture note: lec_notes_0923
next lecture note: lec_notes_0928

Main class wiki page: home

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.

Main Points

Steps to the Analytic Method:

1) 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>

<math> \hat{H}=\frac{p^2}{2m}+V(x)=-\frac{\hbar^2}</math>

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

2)

To go back to the lecture note list, click lec_notes
previous lecture note: lec_notes_0923
next lecture note: lec_notes_0928

classes/2009/fall/phys4101.001/lec_notes_0925.1254084987.txt.gz · Last modified: 2009/09/27 15:56 by x500_bast0052