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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.
  

In lecture, we just went over the basics of angular momentum and how it compared to the equations (concepts) we previously learned for the simple harmonic oscillator (SHO).

no top rung

<math>a_\pm ={ \frac{1}{sqrt{2m{\hbar}{\omega}}}(\mp{ip}+m{\omega}x)</math>

bottom rung, <math>{a_-}{\psi}=0</math>

<math>[a_+,a_-]=-1</math>

<math>H = {\hbar}{\omega}({a_+}{a_-}-1)</math>

has a top rung, <math>{L_z}{f_t}={\hbar}{l}{f_t}</math>; <math>{L^2}{f_t}={\lambda}{f_t}</math>

<math>L_\pm =\pm{i}{\hbar}L_y + L_x</math>

bottom rung, <math>{L_z}{f_b}=-{\hbar}{l}{f_b}</math>; <math>{L^2}{f_b}={\lambda}{f_b}</math>

The hamiltonian, H, is proportional to

<math>[L_+,L_-] = 2{\hbar}{L_z}</math>

<math>L^2 = {L_\pm}{L_\mp}+{L_z}^2\mp{\hbar}{L_z}</math>

To go back to the lecture note list, click lec_notes
previous lecture note: lec_notes_1111
Main quiz 3 concepts: Quiz_3_1113
next lecture note: lec_notes_1118