# Paradigms in Physics

## PH427: Periodic Systems

In Spring 2013 the course is being taught Week 5 - Week 7 by Prof. Ethan Minot. The course is part of the Paradigms in Physics series.

## Calendar

#### Week 5

1MIntroduction. Pair of coupled oscillatorsClassnotes1, 2013. Prepare for analyzing more complicated “many oscillator” systemsTaylor Ch 11 p417-430
2TuNatural frequencies and normal modes. Classnotes2, 2013. Worksheet1, Normal modes simulation, graph_paper.pdf
3WDispersion for 1d mass/spring systemClassnotes3, 2013. Wavenumber k. Continue the worksheet hw1, hw1 soln
4ThDispersion for 1d mass/spring systemClassnotes4, 2013. Solving the infinite chain. First Brillioun Zone, Deybe frequency, Speed of sound. Fixed end point boundary conditions vs. periodic boundary conditions.
5FLattices at finite temperatureClassnotes5, 2013, molecular dynamics movie, Bose-Einstein statistics, phonon number hw2, hw2 soln

#### Week 6

6MPhonon Dispersion & heat capacityClassnotes6, 2013.Discuss the coupled pendulum system. Review the definition of a phonon. Calculate total vibrational energy in a lattice.Heat capacity
7TuLattices (final topics)/electron wavefunctions (intro)Classnotes7, 2013. Analyze the 1d diatomic lattice. Transition to quantum mechanics. Introduce the one-electron wave function for a double-well potential.
8WDouble potential wellClassnotes8, 2013. Find eigenstates and eigenenergies for a double well system in terms of the single well ground states and the overlap intergral. McIntyre Ch15hw3, hw3 soln
9ThLinear combination of atomic orbitalsClassnotes9_2013. Worksheet2. Band structure simulation. Use the computer simulation to explore eigenstates and eigenenergies for 1 well up to 10 wells. McIntyre Ch15Proposed Journal Club Talks due
10FLinear combination of atomic orbitalsClassnotes10_2013. Example of journal club presentation. Derivation of dispersion relationship for LCAO electron eigenstates. Boundary conditions: fixed end vs. periodic.McIntyre Ch15hw4, hw4 soln

#### Week 7

11MLinear combination of atomic orbitalsClassnotes11_2013. Kinesthetic activity: What does an LCAO wave state look like? Similarities/differences with vibrational normal modes. First Brillioun Zone. Bloch oscillations.McIntyre Ch15
12TuLinear combinations of atomic orbitalsClassnotes12_2013. Bands formed from other atomic orbitals (beyond the ground state orbital). Filling of bands with electrons. Metals vs. insulators vs. semiconductors. Light absorption due to electronic transitions. Density of states worksheetMcIntyre Ch15
13WJournal Club Talks
14ThJournal Club TalksClassnotes14_2013. Quiz question about transparency. Analytical expression for density of states.
15FReview sessionReview session 2013 hw5,hw5 soln

Web pages from previous years