This course will develop the wave function approach to relativistic quantum mechanics as originally formulated by P.A.M. Dirac. The energies considered will be below the energy required for electron positron pair creation. Thus, relativistic quantum field theory (RQFT) will not be introduced in this course. However, this course will be helpful to prepare for any future RQFT.
1. The Lorentz metric. The Klein -Gordon equation.
2. The Dirac equation. The relativistic action.
3. Dirac equation for a particle in an EM field. Covariance of the Dirac equation.
4. More on covariance.
5. Heisenberg picture in QM. Constants of the motion. Velocity and position.
6. Total angular momentum. The existence of the spin.
7. Explicit plane wave solutions.
8. Theory of the positron. Antimatter.
9. Transition to polar variables. Central potentials.
10. The hydrogen atom. Exact energy levels. Fine structure.
11. Spin orbit coupling.
12. Energy levels for an electron in a constant magnetic field.
P. A. M. Dirac, “The principles of Quantum Mechanics “ 4th Revised Edition.
OXFORD University Press ISBN: 0 19 852011 5