Advanced Quantum Mechanics (Quant3)

Knowledge:

The course gives knowledge about the modern quantum mechanics formalism, including Dirac notation, density matrices, different representations (such as e.g. position and momentum representations), and the importance of symmetries for conservation laws and practical solutions of quantum mechanical problems. Furthermore, the principles of scattering theory and time-dependent perturbation theory is an important part of the course, as well as introductions to relativistic and many-particle states.

Skills:
The course should provide the student with the ability to:

• Understand a quantum mechanical description of physical systems.
• Solve  both time-dependent and time-independent
  simple examples of quantum mechanical problems using the Dirac formalism.
• Use the concept of propagators and understand Feynman's method of path integrals.
• Use symmetry arguments to simplify the c.alculations and to understand the corresponding conserved quantities
• Calculate scattering amplitudes using advanced scattering theory
• Formulate and perform calculations on many-body problems in terms of second quantization.
• Understand the relativistic Dirac equation and its relation to non-relativistic quantum mechanics.

Competences:
This course will provide the students with the necessary background for further studies in the different topics of quantum physics, such as quantum optics, condensed matter physics and particle physics, and it will give the student some of the necessary tools needed for analyzing physical systems where quantum mechanical effects play an important role. Students will also be introduced to simple quantum computations that allow us to illustrate and probe the behavior of quantum systems.