Archive, 2012

PH427: Periodic Systems

In Spring 2012 the course is being taught Week 8 - Week 10 by Prof. Ethan Minot. The course is part of the Paradigms in Physics series.


Week 8

DayTopicSummaryAdditional ReadingAssignments
1MIntroduction. Pair of coupled oscillatorsClassnotes1. Prepare for analyzing more complicated “many oscillator” systemsTaylor Ch 11 p417-430
2TuNatural frequencies and normal modes. Classnotes2. Worksheet1, Normal modes simulation, graph_paper.pdf
3WDispersion for 1d mass/spring systemClassnotes3. Wavenumber k. Continue the worksheet hw1, hw1 solns
4ThDispersion for 1d mass/spring systemClassnotes4. 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, molecular dynamics movie, Bose-Einstein statistics, phonon number hw2, hw2 solns

Week 9

DayTopicSummary Additional ReadingAssignments
7TuLattices (final topics)/electron wavefunctions (intro)Classnotes6. Calculate lattice heat capacity - high temperature limit & low temperature limit, analyze the 1d diatomic lattice, introduce one-electron wave functions in periodic potentials.
8WDouble potential wellClassnotes7. Find eigenstates and eigenenergies for a double well system in terms of the single well ground states and the overlap intergral. McIntyre Ch15hw3, hw3 solns
9ThLinear combination of atomic orbitalsClassnotes8. 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 orbitalsClassnotes9. Journal club example presentation. Finish worksheet. Start derivation of dispersion relationship.McIntyre Ch15hw4, hw4 solns

Week 10

DayTopicSummary Additional ReadingAssignments
11MLinear combination of atomic orbitalsClassnotes10. Finish derivation of dispersion relation. Exercise applying boundary conditions and the dispersion relation.McIntyre Ch15
12TuMetals vs. Insulators. Density of StatesClassnotes11. Different atomic orbitals lead to different bands. Filling of states leads to metallic or insulating behavior. Metallic hydrogen. Density of states. McIntyre Ch15
13WJournal Club Talks
14ThJournal Club Talks
15FReview sessionClassnotes12 hw5, hw5 solns

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