Course Info, Winter 2013

Course summary

PH424/524 is a course about waves. The basic language is developed in the context of harmonic (sinusoidal) waves, and these basic building blocks are used to build other waveforms and pulses. The context is mechanical and electrical waves to study non-dispersive systems, and quantum mechanical systems (Schroedinger equation) to study dispersive systems. In the quantum mechanical system, the formal mathematics is presented in both Dirac notation (similar to PH425) and in terms of the spatial wave function, which looks very similar to the classical systems. The language and interpretation are new and interesting. The QM part is closely related to PH425, Spins and Quantum Measurement. Course activities include one integrated laboratory, group problem solving activities, Maple worksheets and lectures. Independent work involves reading and homework assignments. It is important that students are familiar with their studies of waves in introductory physics (e.g. Knight, Ch 20 and 21), and the solution of Schroedinger's equation in the infinite well from PH314.

By the end of the course students should:

  • master the basic quantities associated with wave motion
  • become familiar with solutions to non-dispersive and dispersive wave equations in the context of electromagnetism, classical mechanics, and quantum mechanics
  • understand the behavior of waves at interfaces (reflection, transmission, impedance) and the behavior in dissipative media (damping)
  • apply the principle of superposition to construct wave packets (and deconstruct using Fourier analysis), and calculate group velocity
  • further develop the basic principles of quantum theory, including eigenstates, measurement, expectation values, probability density
  • further develop the mathematical techniques of separation of variables, superposition, Fourier analysis
  • refine their problem-solving methodology, the foundation for a physicist's approach to the investigation of physical phenomena


Main Instructor: Prof. Ethan Minot (rhymes with not)

  • Office hours: Mon, Wed, Fri 2-3pm.

Teaching assistant: Daniel Gruss

  • Office hours: TBA


You should have taken PH211, 212, 213 and PH314, and the pre- and co-requisite math courses. If you have missed any of the preceding Paradigms, please see the instructor. We will build on concepts and mathematical techniques from previous Paradigms as well as the Paradigms Preface week.

Meeting Times

  • Mondays, Wednesdays and Fridays: 1 pm to 1.50 pm in 212 Weniger Hall
  • Tuesdays and Thursdays: 12 pm to 1.50 pm in 212 Weniger Hall

Please note: Food and drink are not allowed in Weniger 212. The only exception is closed lid water bottles. Contact the instructor if you have health reasons to require food during class time (for example, diabetes).

Text books

The Paradigms in Physics website has details about all the text books that are used during the year. Ph424 draws from many of these text books:

  • Main, “Vibrations and Waves in Physics”, 3rd edition, Cambridge University Press, 1993.
  • Griffiths “Introduction to Electrodynamics”, 3rd edition
  • McIntyre, “Quantum Mechanics: A Paradigms Approach”, 1st edition.
  • Taylor, “Classical Mechanics” (2005)

There is also a growing number of free webpage resources related to ideas covered in ph424.


Students in the College of Science should have access to a free copy of Mathematica.

Download page

Course Evaluation:

Homework 30%
Laboratory portfolio 20%
Final 50%

Required homework problems will be graded. Assignments are posted on the class webpage. Solutions will be posted immediately after class, on the due date. Assignments turned in after solutions are posted may earn partial credit; you should always inform the instructor or TA beforehand if assignments will be late and explain why. Turn in partially completed assignments by the due date and the rest later for possible partial credit. Pay attention to your presentation - clarity, neatness, and logical structure contribute to the overall assessment. Make your solutions a model that a beginning sophomore in physics could work from. Collaboration on homework is encouraged, but write-ups must be completely and absolutely independent. If you find that you have worked on a problem for 1/2 hour without making any progress, it would be a good idea to stop and seek help. Practice problems provide simple examples for you to check whether or not you understand the material as we go along. They will not be graded.

There is one laboratory that is part of the course. A complete laboratory portfolio includes records of data and computations. Laboratory and computer exercises are performed in teams, but each student must be responsible for his or her own report.

The final exam involves problems mostly similar to those encountered in the homework assignments, and in the physical and computational laboratory experiences. (No Mathematica or other programming will be required). As usual in the Paradigms, the final will be held on the Monday evening following the last day of class.

Students with Disabilities

Students with documented disabilities who may need accommodations, who have any emergency medical information the instructor should know of, or who need special arrangements in the event of evacuation, should make an appointment with the instructor as early as possible, no later than the second day of the class.

link for instructors