Midterm, Feb 19: midterm preparation; Quiz.

Our midterm will be on February 19. I'll post more regarding what to study and emphasize, and how I would suggest you prepare for that, etc. The following is a rough guide and a start to that conversation. Basically, our primary point-of-reference and guide is the homework problems, but we can flesh that out a little.

I think it is a good idea to be familiar with almost all of the energy eigenstate wave-functions we have discussed. These include:
the first 3 states of the 1D harmonic oscillator,
the first 3 states of the 1D infinite square well placed between x=0 and x=L,
the first 3 states of the 1D infinite square well placed between x=-L/2 and x=L/2 (we haven't actually looked at this one yet, but I think you should know these states as well),
the ground state of hydrogen,
the 4 excited states of hydrogen in the r, x, y, z notation.
For good measure I would add:
the states associated with the first 3 energy levels of the 2D harmonic oscillator, and,
the states associated with the first 2 energy levels of the 3D harmonic oscillator (1 ground state + 3 1st-excited states).

Quantum mechanics is pursuit that takes you into the world of eigenfunctions. If you don't learn to hear and understand their language, you will be lost.  Time spent with eigenfunctions (wave-functions) is time well spent. If you can forget them, then your relationship is not sufficiently intimate. It goes without saying that you would wish to know the energies of each of the above states and how to use that to add in their time dependence. (All quantum states are time dependent.)

Additionally, you would like to know how to calculate expectation values for an electron in one of these states, or in some simple combinations of them. One would also wish to have a reasonable understanding of what expectation values are trying to communicate.  And also, to understand how and why expectation values for mixed states tend to be time dependent, while those calculated for energy eigenstates are not.

To help you assess your depth of understanding and your ability to communicate that in a test-type format, I think we should have a quiz soon. I am thinking of a closed book, one or one-a-half hour quiz. You may use one page of notes. (Your page of notes should have only basic stuff, eigenfunctions, energies, operator definitions, etc., not because you don't know them by heart, but just to reassure you when you are working in a stressful situation. Also a bunch of definite integrals*,  but no solved problems please.) I think that taking this quiz in a simulated test environment in your own home may help you gauge your readiness for the midterm. Please let me know when you think you can be ready.