Quantum physics - 4PMNPHQ9

Goal(s)

This second course in quantum mechanics will deepen the physical concepts describing the microscopic properties of materials and devices. A brief introduction to lagrangian mechanics will allow us to go into the foundations of quantum mechanics. We will then apply the tools from kinetic momenta to exactly calculate the energy levels of a charged particle in a Coulomb potential (Hydrogen atom). Going further usually requires approximations. Perturbation theory is one example of fundamental importance and its time-dependent version allows understanding transition probabilities between states (Fermi golden rule). We then use this for an introductory description of the interplay of matter and electromagnetic radiation. We conclude with a chapter on scattering theory.

Content(s)

• Introduction to analytical mechanics. Lagrangian, conjugate variables, hamiltonian, quantization.
• The harmonic oscillator (exercise session).
• Kinetic momentum in quantum mechanics. Quantum numbers, electron spin, addition of momenta.
• Quantum description of the hydrogen atom.
• Time-independent perturbation theory. Degenerate/non-degenerate case.
• Time-dependent perturbation theory. Example of constant perturbation of a harmonic oscillator. Fermi golden rule.
• Introduction to second quantization: atom in an electromagnetic field. Absorption, spontaneous/stimulated emission of photons.
• Scattering theory.

• Principles of quantum mechanics, Schrödinger equation
• Dirac formalism in hermitian vector space.