Periodic Systems

General: Quantum waves in position and momentum space; Bloch waves in one-dimensional periodic systems, and the reciprocal lattice; coupled harmonic oscillators; phonons.

Course Credits

PH 427: Paradigms in Physics: Periodic Systems meets 7 hours per week (MWF for 1 hour, TR for 2 hours) for five weeks for a total of 3 credits.

Prerequisites, Co-requisites and Enforced Prerequisites

Prereq: PH 424, PH 425; coreqs: PH 315

Office Hours

(inst) TBA



Learning Resources

Required textbooks:

  • Classical Mechanics by J. Taylor
  • Quantum Mechanics: A Paradigms Approach by David McIntyre


Course Content

Quantum free particle
Position and momentum space; uncertainty principle
Wave packets and group velocity
Coupled harmonic oscillators; normal modes
Periodic systems and the unit cell
Periodic coupled harmonic oscillators; phonons and dispersion relations
Acoustic and optical phonons
Scattering from barriers (transmission, reflection, and tunneling)
Coupled finite square wells
Bloch's theorem
Periodic nite square wells and band structures
Journal club presentations

Systems of equations
Matrix representation of coupled ordinary differential equations
Generalized eigenvalue problems
Step functions and Dirac delta functions

Student Learning Outcomes

Students shall be able to:
Apply the principle of superposition to construct wave packets and calculate group velocity
Move fluently between position and momentum space
Use the uncertainty principle to estimate the magnitude of quantities
Explain how periodic symmetry relates to the conservation of crystal momentum
Solve for the normal modes and frequencies of a set of coupled harmonic oscillators
Solve for 1D energy eigenstates of stepwise constant potentials
Interpret band structures and dispersion relations, including finding the group and phase velocities
Read and summarize a scientific research paper
 Give a clear oral presentation

Evaluation of Student Performance

  • The grade will be determined by
    1. 15% Journal club oral presentation
    2. 15% Announced quizzes
    3. 35% Weekly homework (including journal club written content)
    4. 35% Final exam

    If a student's grade on the finnal exam is better than that of their average on quizzes, the final exam grade will replace their quiz grade. Late homework is not accepted, but the lowest week's homework grade will be dropped.

How to submit homework--Gradescope

Instructions are coming!!!  They will be posted here when available.

Statement of Expectations for Student Conduct

Students will be expected to abide by all university rules regarding student conduct and academic honesty, in particular, see: link to University Rules.

Statement Regarding Students with Disabilities

Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.