Elements of analytical mechanics, quantum mechanics and special relativity

• Analytical mechanics :
  • Euler-Lagrange equation, generalized coordinates, constant of the motion, Lagrange constraints and multipliers.
  • From Lagrandian to Hamiltonian, Hamilton equations, Poisson brackets, canonical transformations.
  • Varationional principle, conservation laws, Noether’s theorem.
  • Lagrangian description of continuous media.

• Quantum mechanics :
  • Postulates, Schrödinger equation, observables and corresponding operators.
  • Coupling of orbital moment, perturbation theory, varationional method.
  • Density matrix, second quantification.

• Special relativity for subatomic physics :
  • Postulates, Lorentz transformations, Minkowski space, lengths contraction and time dilation.
  • Energy-monentum quadrivectors and relativistic kinematics.
  • Dirac equations, derivation, formulation with gamma-matrices and solutions.