The course re-presents quantum mechanics using Dirac's notation with emphasis on quantum amplitudes and operator methods. Two problem sets will be issued

1. Dirac notation

• 1.1 Quantum amplitudes
• 1.2 Vector spaces and their adjoints
  • 1.2.1 Changes of basis
• 1.3 Operators and observables
  • 1.3.1 The identity operator and functions of operators
  • 1.3.2 Hermitian adjoints
  • 1.3.3 Commutators
• 1.4 The position representation
• 1.5 The energy representation
• 1.6 Conserved quantities

2. Harmonic oscillators

• 2.1 Motion in a magnetic field

3 Angular momentum

• 3.1 Spin-half
• 3.2 Spin one
• 3.3 Orbital angular momentum
• 3.4 Addition of angular momenta
  • 3.4.1 Kets for composite systems

4. Perturbation theory

• 4.1 Time-independent perturbations
  • 4.1.1 Normal Stark effect
  • 4.1.2 Anomalous Stark effect
• 4.2 Time-dependent perturbations
  • 4.2.1 Fermi's golden rule; Born scattering cross section
  • 4.2.2 Adiabatic principle