Nov 02 (Mon) Main Topics in Chap 4, Separation variables for Spherical coordinate [Physics Intranet]

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Nov 02 (Mon)

Responsible party: Captain America, David Hilbert's hat

To go back to the lecture note list, click Lecture Notes
previous lecture note: Oct 30 (Fri) Uncertainty Principle
next lecture note: Nov 04 (Wed) Laplacian in Spherical Coordinate, Legendre Polynomals

Main class wiki page: Physics 4101.001 QM wiki page

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:

$\nabla^2$ spherical coordinates
$L^2, L_z$ , 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: $[-\frac{\hbar^2}{2m}\frac{ \partial^2}{ \partial x^2} + V(x)]\psi=E \psi$

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

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

Where $\nabla^2$ is equal to $\frac{ \partial^2}{ \partial x^2} + \frac{ \partial^2}{ \partial y^2} + \frac{ \partial^2}{ \partial z^2}$

To Be Finished:

Discussion on The Angular Equation
Legendre Polynomials

To go back to the lecture note list, click Lecture Notes
previous lecture note: Oct 30 (Fri) Uncertainty Principle
next lecture note: Nov 04 (Wed) Laplacian in Spherical Coordinate, Legendre Polynomals