Outline

Here is a working outline for our class so you can have an idea what i am thinking about in terms of what we may be doing next (as well as what we have done and are focused on now).  From time-to-time I can add discussion here regarding what you may wish to think about to prepare for our upcoming topics.

For example. I think the next topic coming up pretty soon is called energy and chemical bonding, but to study that one really needs to understand energy in quantum physics more generally. Just as in the physics 5 series, one can study energy by dividing it into two parts: kinetic and potential. These can abbreviate as K.E. and P.E., or just T and U. For example, what is the expectation value of the kinetic energy of an electron in the ground state of an infinite square well? How about its potential energy? Why does the ground state wave-function of a finite square well spill out beyond the edges of the well? What is the motivation for that? Closely related questions have to do with the size of the g.s. wave-fucntion for the harmonic oscillator or the hydrogen atom?  Why are they not smaller?

Then we can consider how to construct molecular wave-functions (from atomic wave-functions) and what the benefit (in terms of energy) of that might be.

Your thoughts, comments and questions are welcome. (One thing to note is that we won't really use the time dependence until we get to the sections on quantum spectroscopy and lasers. For now, we are still focused on energy eigenstates (wave-functions), which are "stationary states".)

1D quantum theory:
 -bound states of 1D systems
 -time dependence and wave-like nature of 1D bound states
 -time dependence of mixed states.

2D quantum theory:
 -bound states of the 2DHO
 -degeneracy
 -time dependence of mixed states in 2D

3D quantum theory:
 -bound states of the hydrogen atom (i.e., of an electron in a -1/r potential)
 -degeneracy of the 1st excited states
 -degeneracy, spin and the periodic table chemical
 -bonding with the 1st excited states,
     --sp2: Hexane, C2H4 sigma bonds (+ the pz orbital which can form pi bonds and delocalize)
     --sp3: diamond and the structure of semiconductors (including Si, Ge, GaAs, GaAlP, GaN…
             -H2O
 - energy and chemical bonding (why H2 has a lower energy than H and H)

Quantum theory of semiconductors:
 -back to 1D models
    --2 square wells
    --an infinite number of square wells
 -electron states of spatially periodic systems
 -Fermi statistics

Quantum spectroscopy:
 -of a 1D sq well with N bound states
 -stimulated absorption of a photon
 -photoelectric effect spectroscopy (photoemission)
 -spectroscopy of a hydrogen atom
    --transitions between quantum states, selection rules
    --fine structure (spin-orbit related splitting)
    --atom in a magnetic or electric field (effect on degenerate states)

Lasers:
 -Bose statistics
 -stimulated emission of photons
 -semiconductor lasers

Additional topics: