Table of Contents
Periodic Systems
In the Periodic Potentials Paradigm, … (more...)
Textbook: Quantum Mechanics: A Paradigms Approach—-a textbook that follows the paradigms approach. The chapters that are relevant to the Periodic Systems course are:
15. Periodic Potentials
Sample Syllabus: PH427 current
Course Contents
Course Project
Unit: Classical waves in periodic systems: the beaded string
Introducing Periodic Systems (50 minutes)
- Identifying Several Periodic Systems (SWBQ, 10 minutes)
- Periodic Systems in Different Dimensions (Lecture, 5 minutes)
- Common Phenomena in Periodic Systems (Lecture, 10 minutes)
- Emulating Waves in a Periodic System (Kinesthetic, 15 minutes)
- Definitions of Important Terms for This Unit (Lecture, 10 minutes)
1-D Chain of Identical Atoms
- Review of Differential Equations in Circuits (Lecture, 5 minutes)
- Single Simple Harmonic Oscillator (SWBQ, 5 minutes)
- Two Coupled Oscillators (Lecture, 30 minutes)
- Coupled Oscillators and the Monatomic Chain (P.S. Lab 1) (Integrated Laboratory, xx minutes)
- Approximating the N-th Normal Mode Frequency for an N-chain Oscillator (Lecture, 10 minutes)
- Infinite Chain of One-Dimensional Atoms (Lecture, 30 minutes)
1-D Chain of Diatomic Molecules
- The Diatomic Chain (P.S. Lab 2) (Integrated Laboratory, xx minutes)
- Infinite Chain of One-Dimensional Diatomic Molecules (Lecture, 40 minutes)
- The Optical and Acoustic Branches of an Infinite Diatomic Chain (Small groups, 10 minutes)
Unit: Internal Energy and Heat Capacity in a Periodic System
Heat Capacity
- Recalling Heat Capacity (SWBQ, 5 minutes)
- Energy Magnitudes for Thermal Processes (SWBQ, 5 minutes)
- Using the Equipartition Theorem to Estimate Heat Capacity (Lecture, 10 minutes)
- Specific Heat of a Sample of Water (SWBQ, 10 minutes)
Internal Energy
- Drawing Bound States (SWBQ, 5 minutes)
- Quantization of Energy in Mechanical Oscillators (Lecture, 15 minutes)
- Predicting the Phonon Number of an Oscillator (SWBQ, 5 minutes)
- Approximating the Internal Energy for a 1-D Chain (Lecture, 30 minutes)
- Approximating the Internal Energy for a 3-D Lattice (Lecture, 30 minutes)
Unit: Quantum Waves in Periodic Systems: The LCAO Method
The 1-D 2-Well Potential Chain
- Differences Between Vibrating Atoms and Electrons in a Crystal (Lecture, 5 minutes)
- Energy Eigenstates of a Single Potential Well (Lecture, 5 minutes)
- Finding the Energy Eigenstates of a 2-Well System (Lecture, 30 minutes)
- Showing Two Vectors are Eigenstates in a 2-Well System (SWBQ, 10 minutes)
- Solving for $\alpha$ and $\beta$ for the 2-well Case (Lecture, 10 minutes)
The 1-D N-Well Potential Chain
- The Periodic Finite Square Well Potential (P.S. Lab 3) (Integrated Laboratory, xx minutes)
- The Hamiltonian for an N-Well System (Lecture, 20 minutes)
- Finding the Energy Eigenstates of an N-Well System (Lecture, 40 minutes)
- Practice With a Linear Combination of Atomic Orbitals (SWBQ, 15 minutes)
- 9 Atomic Wells (Kinesthetic, 15 minutes)
- Periodic Boundary Conditions on Long Chains of Atoms (Lecture, 15 minutes)
Insulators and Conductors
- Single Electron in a Crystal (Lecture, 15 minutes)
- Half-Filled Electron Band in a Crystal (Lecture, 10 minutes)
- Filled Electron Band in a Crystal (Lecture, 10 minutes)
- Effective Mass (Lecture, 10 minutes)
