Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 8
Symmetries, conserved quantities, and the labeling of states
Angular Momentum
Todays Program:
1. Symmetries and conserved quantities labeling of states
2. Ehrenfest Theorem the greatest theorem of all times (in Prof. Anikeevas opinion)
3. Angula
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 11
Waves in Periodic Potentials
Today:
1. Inverse lattice definition in 1D.
2. Graphical representation of periodic and aperiodic functions using the kaxis and
inverse lattice vectors.
3. Series solutions to the periodic potential Hamiltonian
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 7
Quantum Mechanical Measurements.
Symmetries, conserved quantities, and the labeling of states
Todays Program:
1. Expectation values
2. Finding the momentum eigenfunctions and the dispersion relations for free particle.
3. Commutator and observab
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 10
Waves in Periodic Potentials
Today:
1. Direct lattice and periodic potential as a convolution of a lattice and a basis.
2. The discrete translation operator: eigenvalues and eigenfunctions.
3. Conserved quantities in systems with discrete tr
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 2
The Hamiltonian approach to classical mechanics.
Analysis of vibrations in onedimensional lattice.
Program:
1. Vibrations of a simple diatomic molecule.
2. Lattice vibrations in a monoatomic 1D lattice: modes and dispersion relations.
Questions
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 4
Introduction to Quantum Mechanical Way of Thinking.
Todays Program
1. Brief history of quantum mechanics (QM).
2. Wavefunctions in QM (First postulate)
3. Schrodingers Equation
Questions you should be able to answer by the end of todays lecture:
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 1
The Hamiltonian approach to classical mechanics.
Analysis of a simple oscillator.
Program:
1. Hamiltonian approach to classical mechanics.
2. Vibrations of an electron in a lattice: simple oscillator
Questions you should be able to answer by the
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 13
Band Diagrams
Today:
1. Analytical expression for bandgaps
2. Group velocity, density of states
3. Counting the number of states per band: periodic boundary conditions
Questions you should be able to answer by the end of todays lecture:
1.
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 15
FermiDirac Distribution
Today:
1. Fermi energy, and momentum, DOS.
2. Statistics of gases.
3. FermiDirac distribution.
Questions you should be able to answer by the end of todays lecture:
1. What are the basic steps used to derive the Fer
Electronic, Optical and Magnetic Properties of Materials
ENGINEERIN 3.024

Spring 2013
Lecture 9 (OnLine Video)
The Hydrogen Atom
Todays Program:
1. Angular momentum, classical and quantum mechanical.
2. The Hydrogen atom semiclassical approach.
3. The Hydrogen atom quantum mechanical approach.
4. Eigenfunctions and eigenvalues common t