Physics current students - Density Matrix Theory

Lecturer: Dr Tim Scholz

This 6 lecture course commences with a discussion of why we need a quantum theory in the first place and then gives a intuitive derivation of the Schroedinger equation based upon an anology with classical mechanics. Next the quantum mechanics of a spin half particle is examined and extended to describe a beam of such particles. The spin polarization vector of the beam is shown to be intricately related to its density matrix. The ability of this density matrix theory to predict the results of any spin experiment performed upon the beam is described. A similar treatment is given to the quantum theory of light. In this case the connection between the classical polarization of light and its quantum mechanical counterpart helicity is first analysed. The relationship between the polarization of the photon beam and its density matrix is described. It is shown that the density matrix can be written in terms of the four Stokes parameters of the beam. The resulting density matrix is then used to predict the results.

The Origin of Quantum Theory
- The Need for a Quantum Theory
- The Schroedinger Equation
Elementary Concepts
- Introduction
- Spin States and the Density Matrix of Spin 1/2 Particles
  - Pure Spin States
  - The Polarization Vector
  - Mixed Spin States
  - The Spin Density Matrix
  - Independent Parameters
  - Paramererization of the Density Matrix
- Polarization and the Density Matrix of Photons
- The Concept of Wave Polarization
- Pure and Mixed Polarization States of Photons
- The Quantum Mechanical Concept of Spin
- The Polarization Density Matrix
- Stokes Parameter Description
General Density Matris Theory
- Pure and Mixed Qunatum Mechanical States
- The Density Matrix and its Basic Properties