Topical Outline and notes.

Below is a topical outline covering at least the next few weeks, and below that some notes related to the outline (filling in some selected details and nuances.)

So far we have covered:
*1D quantum wave-functions, with an emphasis on spatial wave-functions, but looking also at energies and time-dependence in missed states. *2 and 3D quantum wave-functions: with an emphasis on degeneracy and combining degenerate states to get novel and important spatial wave-functions, e.g., sp2 *Periodic table: with an emphasis on sp hybridization and the 2nd row. *Energy in quantum physics: with an emphasis on quantum kinetic energy and its relationship to confinement. (In most of the above, expectation value calculations have played a significant role in our understanding.) ------

Topical Outline:
*States in molecules
*States in crystals *
   Bands of states (including mention of velocity of packets formed from band states)
   Filling of band states
   Metals Fermi function, Fermi energy
   Electric field and conductivity. ( a few electrons moving really fast)

*Semiconductors:
  Valence and conduction bands
  Electrons and holes carriers from optical excitation, temperature and doping.
  p-n junction LEDs, LASERs and solar cells

Spectroscopy:
  H atom
  length scales of light and the atom
  inducing mixed states (E field)
  fine structure, spin-orbit coupling

Notes: States of molecules and crystals: we will explore how to use wave-functions from our study of atoms to create wave-functions appropriate for molecules and crystals. Using energy bands in one-dimensional crystals as a starting point and a reference point we will examine the origin of energy bands in crystals and examine the states that belong to a particular band. Look at how they are formed and in what ways they are similar to each other and in what ways they are different. This will allow is to explore the natures of metals, semiconductors and insulators, as well as things like electrical conductivity and optical transitions in metals, semiconductors and insulators. We will see how the color of copper and gold can be connected to the Schrodinger equation. Fermi statistics in metals and semiconductors: We will see how metals have a Fermi surface with very energetic electrons, and how current in a metal involves a few very-fast moving electrons (fewer electrons than you might expect, each moving faster than expected). In semiconductors we will delineate the valence and conduction bands, and talk about optically created carriers (photoconductivity), as well as finite temperature and doping. Then p-n junctions and p-n junction lasers, leds and solar cells.

Difficulties of solving and understanding systems with many interacting electrons. Limits on using the Schrodinger equation to understand complex or strongly interacting systems. More is different is an important concept that helps define what is important and challenging in physics and the difficulties of going further than we have with the Schrodinger equation or any reductionist approach.

Back to the hydrogen atom, we will look at spin-orbit splitting (which is part of what is called fine structure). In this we see the importance of a new interaction term in producing new results and physics. We will revisit spin and consider its obtuse relationship to angular momentum. This will include another look at atomic spectroscopy and the $\psi_{n,l,m}$ states.