Paradigms in Physics: Periodic Systems | 2026-Spring

Course Name
Paradigms in Physics: Periodic Systems
Course Number
PH 427 / PH 527
Year/Term
2026
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Course Credits
4
Class meeting times
9 hours of lecture/discussion per week for five weeks.
Prerequisites
PH424, PH425
Course description
Quantum waves in position and momentum space; Bloch waves in one-dimensional periodic systems, and the reciprocal lattice; coupled harmonic oscillators; phonons.

Topic/Day

Activities

Resources

Homework Due

Day 1
Welcome & Overview
Liz's OneNote Notebook
Fun with Translation Operators
Intro to Discrete Translation Operator
Eigenvalues \& Eigenvectors of $\hat{S}^{\uparrow}$ (5 Beads)
Reading: GMM Discrete Translation Operations
Reading: GMM Powers and Roots of Complex Numbers
Day 2
2 Symmetric Coupled Oscillators
Two Oscillating Masses - Same Mass, 2 Different Springs
Reading: Taylor 11.1,2
Coupled Oscillations Mathlet
Normal Modes PhET
Reading: Taylor 11.3,7
Day 3
Gaussian Functions
Gaussian Parameters
Reading: GMM Gaussians
HW 1 w/Solution
Normalization of the Gaussian
DELETE Normalization of the Gaussian for Wavefunctions
Reading: GMM Normalization of Gaussians
Day 4
Review Fourier Series
Definition of Fourier Transform and Inverse

Reading: GMM: Fourier Transforms

Reading: McIntyre Appendix D - Waves & Fourier Analysis

Fourier Transforms
Fourier Transform of the Delta Function
Fourier Transform of a Gaussian
Fourier Transform of a Plane Wave

Wolfram Fourier Transform Calculator

Making Waves PhET

Reading: GMM: Fourier Transform of the Delta Function

Reading: GMM: Examples of Fourier Transforms

Day 5
More Fourier Transforms
Fourier Transform of a Shifted Function
Fourier Transform of a Derivative
Reading: Properties of the Fourier Transform
HW 2 w/Solution
Day 6
Core Quantum Questions
Review Quantum Systems
Core Quantum Questions
Wave Particle Duality
Wave–Particle Behavior in Nature
Energy Eigenvalue Equation and Wavefunction
Free Particle Wave Equation
McIntyre 5.2,3
Day 7
Bound States for the Infinite Square Well
McIntyre 5.4
Qualitative (Eyeball) Solutions for a Bumpy Well
Asymmetric Well
Reading: McIntyre 5.10.1
Delta Function Potential Well
Delta function potential boundary condition
Day 8
Bound States for the Finite Well
Solving the Energy Eigenvalue Equation for the Finite Well

Reading: McIntyre 5.5, 5.10.1

Bound States PhET

HW 3 w/Solution
Day 9
Free Particle
McIntyre 6.1
Free Particle Energy Eigenstates
Free Particle Energy Eigenstates
Free Particle Momentum Eigenstates & de Broglie Wavelength
Momentum Eigenstates of the Free Particle
Time Evolution of the Free Particle Eigenstates
Normalization of the Free Particle
Day 10
Intro to Momentum Space
Intro to Momentum Space
McIntyre 6.1
HW 4 w/Solution
Day 11
Momentum Representation Operators
Momentum Representation of Operators
Momentum Representation Wavefunctions
Momentum Representation of the Energy Eigenstates of the Infinite Square Well
Day 12
Intro to Wave Packets: Discrete Superposition
Discrete Superposition of Energy Eigenstates of the Free Particle
Gaussian Wave Packets

Reading: McIntyre 6.2

Wave Packet PhET

Day 13
Uncertainty Principle
Estimating Energy with the Uncertainty Principle: Harmonic Oscillator
Estimating Energy with the Uncertainty Principle
Reading: McIntyre 6.3
Day 14
Unbound States & Scattering
Scattering off a Finite Step
Reading: McIntyre 6.4
Day 15
Tunneling Through Barriers
Scattering for the Finite Well Sim
Scattering for a Finite Well
Reading: McIntyre 6.5
Day 16
Coupled Oscillators Review
Taylor 11.1,2,3,7
Day 17
Ring of 4 Oscillators
Four Masses on a Ring
Day 18
Normal Modes & Translational Symmetry
Eigenvalues \& Eigenvectors of $\hat{S}^{\uparrow}$ (5 Beads)
Eigenvectors of $\hat{S}^{\downarrow}$
Day 19
N Oscillators
Reading: Taylor 11.5
Infinite Oscillators in a Ring
Day 20
Phonons
Day 21
LCAO: Energy Eigenstates of a Two-Well Chain
LCAO: Two Delta Wells
Finding the Energy Eigenstates of a 2-Well System
Solving for Hamiltonian Matrix Elements the 2-well Case
Reading: McIntyre 15.1.1
Day 22
LCAO: Energy Eigenstates of an N-Well Chain
Infinite Chain of One-Dimensional Atoms
Hamiltonian for the n-well System
Finding the Energy Eigenstates of an N-Well System
Reading: McIntyre 15.1.2
Day 23
Band Structure
Reading: McIntyre 15.4
Day 24
Bloch's Theorem & the Molecular States
Reading: McIntyre 15.5
Density of states
Reading: McIntyre 15.7
Day 25
Review
Final Exam
Final Exam Schedule
OSU Final Exam Schedule
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Review
OSU Final Exam Schedule