List of topics

• Introduction

  • Postulates of quantum mechanics

• Path integrals

  • Basic idea

  • Free particle propagator

  • Derivation of the path integral

  • The importance of the classical path

  • Other applications: interference experiments and statistical mechanics

• Two body problem and central potentials

  • Moving from 1D to 3D

  • The two-body problem

  • Symmetries of the Hamiltonian and conserved quantities

  • Angular momentum operators reminder

  • Orbital angular momentum has integer values

  • Spherical harmonics: Part 1 and Part 2

  • Diatomic molecules

  • The radial part of the 2 body problem

• Hydrogen atom

  • Back of the envelope hydrogen atom

  • Radial Schrödinger equation

  • General properties of the H atom wavefunctions

  • Laguerre polynomials

• Other examples of central potentials

  • 3D harmonic oscillator including with operator methods

  • Finite spherical well: Part 1, Part 2

  • Infinite spherical well

• Perturbation theory

  • Non-degenerate and degenerate perturbation theory and application to the Stark effect in hydrogen: Part 1 and Part 2

  • The role of Symmetry breaking in degenerate perturbation theory.

  • The ammonia molecule as an example system that transitions from non-degnerate to degenerate perturbation theory.

  • The spin-orbit interaction in hydrogen.

• Identical particles

  • Exchange symmetry and spin-statistics theorem

  • The helium atom: ground state, first excited state and perturbation theory approach

  • The variational method applied to helium

• Scattering

  • Overview: scattering amplitude, differential cross-section

  • Born approximation: Part 1 and Part 2

  • Partial wave expansion

• Time-dependent perturbation theory and atomic transitions

  • Time-dependent perturbation theory and Fermi’s Golden Rule

  • The electromagnetic field in quantum mechanics

  • Second quantization

  • Decay rate of the 2p-state in hydrogen