Classical mechanics:
Lagrangians, the action principle and the E-L equations of motion. The Hamlitonian and Hamiltons canonical equation of motion. Small oscillations. Motion in a central force field. Rigid body dynamics -- the symmetric top. Canonical transformations, the action angle formalism and the Hamilton-Jacobi equation.
Quantum Mechanics:
Linear vector spaces, operators, the bra-ket notation. One dimensional square well and barrier. The simple harmonic oscillator -- using both coordinate space and operator based methods. Angular momentum - spectrum and addition. The hydrogen atom problem. Time evolution, Schrodinger, Heisenberg and interaction picture. Scattering theory. Relativistic quantum mechanics -- the Klein-Gordon and Dirac equations. Relativistic covariance of the Dirac equation and the spin of the electron. |