### Table of Contents

# Paradigms in Physics

## PH424: 1d Waves

In Winter 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 | Intro to waves | Basic vocabulary & concepts. Demo “the wave machine”. Traveling & standing waves. Phase, group, and material velocity. Instructor's lecture notes day1.pdf | Main 9.1, 9.3; Grif. EM 9.1.1, 9.1.2 | |

2 | Tu | Solution to wave equation | Non-dispersive wave equation. Initial conditions, boundary conditions. Dispersion relation. Standing wave demo/lab. Standing wave/dispersion worksheet. Newton's law: Waves in a rope. Instructor's lecture notes day2.pdf | Main 9.0; Grif. EM 9.1.1; Taylor 16.1-16.3 | |

3 | W | Propagation of waves | Examples of non-dispersive systems vs. dispersive systems. Reflection and transmission from a boundary of two materials. Instructor lecture notes day3.pdf | Main 9.2; Grif. EM 9.1.3 | hw1 |

4 | Th | Lab experiment | Complete reflection and transmission coefficients. Impedance. Propagation of waves in a coaxial cable. Data acquisiton, class discussion & analysis. Experiment guide,Guidelines for write up. Instructor lecture notes day4.pdf. | Main 9.5, 10.3; Grif. EM 9.2.1 | |

5 | F | Propagation of waves | Propagation & attenuation. Analysis continuation. Attenuation. Instructor notes day5.pdf | Main 9.2; Grif. EM 9.1.3 | hw2 |

#### Week 6

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

6 | M | Energy in waves | Kinetic energy density, potential energy density. Total energy. Instructor lecture notes day6.pdf. | Main 9.4 | |

7 | Tu | Superposition of waves | Energy density worksheet. Superposition & Fourier analysis. Superposition worksheet. Instructor lecture notes day7.pdf | Main 11.1-11.3; PH 421 notes | |

8 | W | Wave Functions in Quantum Mechanics | The wave function. Probability density. Position, momentum & energy operators. Operators worksheet. Instructor lecture notes day8.pdf | McIntyre 5.1-5.3 | hw3 |

9 | Th | Wave equation in quantum mechanics | The finite square well. Eigenvalues, eigenfunctions of bound states of a finite well potential. Instructor lecture notes day9.pdf | McIntyre 5.2-5.6 | |

10 | F | Quantum states | Review the finite square well. Probability density, expectation values, normalization. Superposition & measurement; square well examples. Instructor lecture notes day10.pdf | McIntyre 5.1-5.6 | hw4 |

#### Week 7

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

11 | M | Quantum states | Superposition & measurement; square well examples. Instructor lecture notes day11.pdf | McIntyre 5.1-5.6 | |

12 | Tu | Time evolution of quantum states | Predicting the outcome of measurements. Time dependence derived from S. Eq and separation of variables. Time development of arbitrary states. Animate on Mathematica. Instructor lecture notes day12.pdf | McIntyre 5.7, 6.1-6.2 | |

13 | W | Time evolution of quantum states + Free particles | Superposition state can radiate light. The Unbound states. Free particles. Instructor lecture notes day13.pdf | McIntyre 6.3 | hw5 |

14 | Th | Scattering | Free particle wavefunctions. Kinesthetic activity. S. Equation is a dispersive wave equation. Wave packets spread out and group velocity differs from phase velocity. Reflection, transmission. Tunneling. Instructor lecture notes day14.pdf | McIntyre 6.4-6.5 | |

15 | F | Tunneling and Review | The WKB approximation. The Heisenberg Uncertainty relation. Instructor lecture notes day15.pdf. topics_for_final.pdf. | McIntyre 6.4-6.5 | hw6 |

The final will be held on Monday evening of Week 8.