# PH427 Periodic Systems

**Course Name:** Periodic Systems

**Course Number:** PH427

**Course Credits:** This course combines approximately 90 hours of instruction, and assignments for 3 credits.

**Prerequisites:** PH 424, PH 425, PH 315 (coreq)

**Course Description: **Many systems in nature, such as crystals, have underlying periodic structures. The periodicity is a special symmetry which leads to many interesting phenomena such as band gap, collective vibrations, etc. We will use quantum mechanics to study how particles, such as electrons, move in a periodic system. We will also study how atoms in a periodic lattice move collectively. The course also has a literature review/presentation component, which will be done by groups of one to two students.

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

**Course Specific Measurable Student Learning Outcomes**:

• 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 magnitude of quantities

• Explain how periodic symmetry relates to 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

**This course is not a Bacc Core Course.**

**Evaluation of Student Performance:**

15% Monday quizzes, 15% Presentations, 35% homework, 35% final exam

• There will be 4 quizzes from week 2-5

• Presentations can be groups of no more than three. Everyone in the same group receive the same grade. The grading of presentation will be done by the whole class based on rubrics given below:

Presentation manner (timing, facing audience, fluent etc) 3pt

Clarity of the background and motivation 3pt

Clarity of the methods 3pt

Clarity of the conclusion and further implications 3pt

Answering questions 3pt

You will read two articles, submit a summary as part of your homework 3 and 5. You will inform us who you are going be presenting with, and your group's choice of article (from what you have written a summary for) together with homework 6. And your group have roughly one week to prepare a 8 - min presentation.

List of journals to look for articles (has to be physics related, preferably condensed matter physics, optics, astrophysics and biophysics)

Nature, Nature Physics, Nature Material, Science, PNAS, Physical Review series (eg. PRL, PRX, PRB, PRE..), Soft Matter

• There will be a total of 10 homework assignments. For each student, the minimal score from the 10 assignments will be excluded when calculating the final score.

Homework 1, 3, 5, 7, 9 are due on Wednesdays of week 1,2,3,4,5

Homework 2, 4, 6, 8, 10 are due on Fridays of week 1,2,3,4,5

Late homework will not be graded, except for medical emergency or prior agreement with the instructor on a case-by-case basis

**Learning Resources**:

Textbook (required): Quantum Mechanics: A Paradigms Approach by David McIntyre

Reference (optional): Classical Mechanics by J. Taylor, Vibrations and Waves in Physics by I. G. Main

**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 http://ds.oregonstate.edu. 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.

The DAS Statement is posted online at: ds.oregonstate.edu/faculty-advisors (4/14/16).

**Student Conduct Expectations link:**

**Tentative schedule:**

### Office hours

- Bo Sun: Monday and Tuesday 2-3 pm, 415A Weniger
- Mackenzie Lenz: Wednesay and Friday 3:00-4:00pm, 304F Weniger
- John Waczak: Wednesday and Thursday 2:00-3:00 pm.

Week 1

1. M. Overview

2. M: Intro to Journal club

3. T: Quantum free particle

4. W: MATH BITS: Step functions and delta functions

5. R: MATH BITS: Fourier transformations

6. F: MATH BITS: Fourier transformations

Week 2

1. M,T: Position and momentum space

2. T: Uncertainty principle

3. W: Wave packets and group velocity

4. R: Scattering from barriers

5. F: Symmetric potentials

Week 3

1. M: Two coupled harmonic oscillators

2. T: MATH BITS: Matrix representation of Coupled ODEs and eigenanalysis

3. W: Properties of coupled ODEs, normal modes

4. R: Few coupled harmonic oscillators

5. F: 1-D solids

Week 4

1. M: 1-D solids, phonons and dispersion relations

2. T: Acoustic and optical phonons -- 1-D solid with two masses

3. W: A toy model for hydrogen molecule, exact solutions

4. R: Linear combination of atomic orbitals

5. R: Electrons in 1-D solids

Week 5

1. M: presentation

2. T: presentation

3. W: presentation

4. R: Metals and insulators, Review

5. F: Review