Responsible party: Captain America, David Hilbert's hat

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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.
  

Class input on main points of the beginning of Chapter 4:

• <math>\nabla\^2</math> spherical coordinates
• <math>L^2, L_z</math>, and why they have discrete values
• The Hydrogen atom model
• How spin affects this
• Degenerate energies and states
• Quantum numbers
  • Where are they from?
  • What do they do?

Using 3-D Coordinates: From the one-dimensional Schrodinger Equation: <math> [-\frac{\hbar^2}{2m}\frac{ \partial^2}{ \partial x^2} + V(x)]\psi=E \psi</math>

The kinetic energy term, <math>-\frac{\hbar^2}{2m}\frac{\partial^2}{ \partial x^2}</math>, must model the 3-Dimensional kinetic energy of the system, and therefore turns into:

<math> [-\frac{\hbar^2}{2m}\nabla^2+ V(x)]\psi=E \psi</math>

Where <math>\nabla^2</math> is equal to <math> \frac{ \partial^2}{ \partial x^2} \frac{ \partial^2}{ \partial y^2} \frac{ \partial^2}{ \partial z^2}</math>

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next lecture note: lec_notes_1104