Quantum mechanics has revolutionized our understanding of the physical world in the 20th century. It has been crucial to advances in fundamental physics, such as the standard model of particle physics, but also is the basis of technological advances ranging from the transistor to the laser. More recently technologies exploiting the properties of individual quantum particles, such as superposition and entanglement, are being explored for technological applications like quantum computing, sensing, and communication.
The aim of this lecture is to provide the tools to tackle advanced and “real-life” problems in quantum theory and quantum technologies and to set the basis for advanced lectures including quantum information theory, quantum optics, condensed matter theory, atomics and molecular physics, and quantum field theory.
Motivated by the goal to understand how quantum technologies, and the qubit as their basic building block, function we will cover the following topics:
- Recap of the postulates of quantum mechanics
- Density operator
- Entanglement
- Quantum channels
- Quantum measurement
- Addition of angular momenta
- Atomic fine and hyperfine structure
- Time-dependent perturbation theory
- Basics of light-matter interactions
- Identical particles
- Quantum description of light
- Many-particle systems
- Dynamics of open quantum systems
- Phase space picture of quantum mechanics
- Scattering theory
Prerequisites:
Solid knowledge of basic quantum mechanics (Quantum theory I)
You should be familiar with:
- Fundamental concepts (bras, kets, operators; base kets and matrix representations; measurements and observables; uncertainty; position and momentum space, wave functions)
- Quantum dynamics (time evolution and the Schrödinger equation; Schrödinger vs. Heisenberg picture; harmonic oscillator; Schrödinger's wave equation)
- Angular momentum (rotations and angular momentum commutation relations, eigenvalues and eigenstates of angular momentum, orbital angular momentum)
- Schrödinger's equation for central potentials (simple examples, idealized hydrogen atom)
- Time independent perturbation theory |
