Table of Contents

# 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

Day | Topic | Summary | Additional Reading | Assignments | |
---|---|---|---|---|---|

1 | M | Introduction. Pair of coupled oscillators | Classnotes1, 2013. Prepare for analyzing more complicated “many oscillator” systems | Taylor Ch 11 p417-430 | |

2 | Tu | Natural frequencies and normal modes. | Classnotes2, 2013. Worksheet1, Normal modes simulation, graph_paper.pdf | ||

3 | W | Dispersion for 1d mass/spring system | Classnotes3, 2013. Wavenumber k. Continue the worksheet | hw1, hw1 soln | |

4 | Th | Dispersion for 1d mass/spring system | Classnotes4, 2013. Solving the infinite chain. First Brillioun Zone, Deybe frequency, Speed of sound. Fixed end point boundary conditions vs. periodic boundary conditions. | ||

5 | F | Lattices at finite temperature | Classnotes5, 2013, molecular dynamics movie, Bose-Einstein statistics, phonon number | hw2, hw2 soln |

#### Week 6

Day | Topic | Summary | Additional Reading | Assignments | |
---|---|---|---|---|---|

6 | M | Phonon Dispersion & heat capacity | Classnotes6, 2013.Discuss the coupled pendulum system. Review the definition of a phonon. Calculate total vibrational energy in a lattice. | Heat capacity | |

7 | Tu | Lattices (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. | ||

8 | W | Double potential well | Classnotes8, 2013. Find eigenstates and eigenenergies for a double well system in terms of the single well ground states and the overlap intergral. | McIntyre Ch15 | hw3, hw3 soln |

9 | Th | Linear combination of atomic orbitals | Classnotes9_2013. Worksheet2. Band structure simulation. Use the computer simulation to explore eigenstates and eigenenergies for 1 well up to 10 wells. | McIntyre Ch15 | Proposed Journal Club Talks due |

10 | F | Linear combination of atomic orbitals | Classnotes10_2013. Example of journal club presentation. Derivation of dispersion relationship for LCAO electron eigenstates. Boundary conditions: fixed end vs. periodic. | McIntyre Ch15 | hw4, hw4 soln |

#### Week 7

Day | Topic | Summary | Additional Reading | Assignments | |
---|---|---|---|---|---|

11 | M | Linear combination of atomic orbitals | Classnotes11_2013. Kinesthetic activity: What does an LCAO wave state look like? Similarities/differences with vibrational normal modes. First Brillioun Zone. Bloch oscillations. | McIntyre Ch15 | |

12 | Tu | Linear combinations of atomic orbitals | Classnotes12_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 worksheet | McIntyre Ch15 | |

13 | W | Journal Club Talks | |||

14 | Th | Journal Club Talks | Classnotes14_2013. Quiz question about transparency. Analytical expression for density of states. | ||

15 | F | Review session | Review session 2013 | hw5,hw5 soln |

Web pages from previous years