Introductory description

The module sets up the relativistic analogues of the Schrödinger equation and analyses their consequences. Constructing the equations is not trivial - knowing the form of the ordinary Schrödinger equations turns out not to be much help. The correct equation for the electron, due to Dirac, predicts antiparticles, spin and other surprising phenomena. One is the 'Klein Paradox': When a beam of particles is incident on a high potential barrier, more particles can be 'reflected' than are actually incident on the barrier.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Introductory Remarks. Revision of relativity, electromagnetism and quantum mechanics; problems with the non-relativistic Schrödinger equation; unnaturalness of spin in NRQM and the Pauli Hamiltonian; phenomenology of relativistic quantum mechanics, such as pair production
2. Klein Gordon Equation. Derivation of the Klein-Gordon equation; continuity equation and the Klein-Gordon current; problems with the interpretation of the Klein-Gordon Equation
3. The Dirac Equation. Derivation of the Dirac equation; the quantum phenomenon of spin; gamma matrix algebra and equivalence transformations
4. Solutions of the Dirac Equation.
   The helicity operator and spin; normalisation of Dirac spinors; Lorentz transformations of Dirac spinors; interpretation of negative energy states
5. Applications of Relativistic Quantum Mechanics.
   The gyromagnetic ratio of the electron; non-relativistic limit of the Dirac equation; fine structure of the hydrogen atom

Learning outcomes

By the end of the module, students should be able to:

• Discuss the general nature of Relativistic Quantum Mechanics
• Solve the Dirac equation in simple cases, and explain its significance and transformation properties.
• Explain how some physical phenomena including spin and the Lamb shift can be accounted for using relativistic quantum mechanics

Indicative reading list

R.Feynman, Quantum Electrodynamics, Perseus Books 1998;
Bethe and Jackiw “Intermediate Quantum Mechanics”, Perseus Books 1997.

View reading list on Talis Aspire

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study