Applied Quantum Mechanics

Overview

1. Why Quantum Mechanics?
2. Particle waves and Schödinger equation
3. One-dimensional examples: potential steps, quantum wells, harmonic oscillator
4. Time-dependent Schrödinger problems
5. Formalism: Hilbert space, state vectors, and operators
6. Approximation methods
7. Time-dependent perturbation theory
8. Angular momentum
9. The hydrogen atom
10. Quantum mechanics of materials

Lectures

1. Why Quantum Mechanics?
   Particle-waves and Schrödinger equation
   Particle in a box
   slides, exercises, and review
2. More one-dimensional examples:
   Potential step
   Bound states in a potential well
   Harmonic oscillator
   Particle in a linear potential
   slides, exercises, and review
3. Time-dependent Schödinger equation
   Time evolution of superpositions of eigenstates
   Wave packets and group velocity
   slides, exercises, and review
   For your entertainment, a podcast entitled Does quantum physics really describe reality? and a simple gnuplot file for plotting the propagation of wave packets.
4. Measurement and expectation values
   Time-evolution operator
   Momentum, position, and Heisenberg uncertainty
   Continuity Equation
   slides, exercises, and review
5. Hilbert space and Dirac notation
   slides, exercises, and review
6. Commutators and uncertaintly principles
   Normalization to a delta function
   slides and exercises
7. Finite basis set
   time-independent perturbation theory
   slides, exercises, and review
   For your entertainment, an article on how birds of passage use quantum mechanics for navigation: Flying home with quantum mechanics
8. tight-binding and variational method
   time-dependent perturbation theory and Fermi's Golden Rule
   slides, exercises, and review
9. nonlinear optical coefficients
   basics of the quantum theory of solids
   (Bloch theorem, band structure, effective mass theory, density of states)
   slides, and exercises
10. band structure: k p method
    optical absorbtion in semiconductors
    slides, and exercises
    A nice Holiday reading: This article by Max Tegmark and John Archibald Wheeler 100 Years of the Quantum, originally published 2001 in the Scientific American, gives a nice overview of the successes of quantum theory and of remaining open questions.
11. angular momentum and spherical harmonics
    slides, exercises, and review
12. The hydrogen atom
    slides, exercises, and review
13. Zeeman effect, electron spin, Pauli matrices, Bloch sphere
    slides and review
14. identical particles, Pauli principle, exchange, and Slater determinants
    Bose-Einstein and Fermi-Dirac statistics
    slides

Textbook

Lecture viewgraphs