# Advanced Quantum Mechanics

Mon, 10.00 - 11.30 | HS IIITue, 8.

**20**- 9.

**50**| HS III

## Overview

The lecture will introduce advanced concepts of quantum mechanics, including- second quantization and field theory
- quantum theory of light
- relativistic quantum mechanics (Klein-Gordon and Dirac equation)
- scattering theory (non-relativistic)
- outlook on quantum information theory

## Tutorials

All tutorials are held on Wednesdays, please check the following**overview**to find your tutorial group.

A special BCGS tutorial will be held Mondays, 12:30-14:00 in seminar room 2 of the new theory building.

**Assignments**

- sheet 0: harmonic oscillator, two-particle wavefunction
- sheet 1: density operator for two spin-1/2, commutators and anticommutators
- sheet 2: Fock-space, two spinful fermions, two particles
- sheet 3: tight-binding Hamiltonian, spin operator in second quantization
- sheet 4: Schwinger boson representation, Bose condensate wavefunction, fermionic Bogoliubov transformation
- sheet 5: Jordan-Wigner transformation, Kitaev chain
- sheet 6: dynamics of field operators, quantization of the electrodynamic fields
- sheet 7: coherent states of the electromagnetic field, Casimir effect
- sheet 8: two fermionic states in a photon-cavity, Lorentz transformations, relativistic electrons
- sheet 9: Klein-Gordon equation, real Klein-Gordon field, parity operator of the real Klein-Gordon field
- sheet 10: γ-matrix identities, Lorentz covariance of the Dirac equation
- sheet 11: Dirac fermions, Weyl fermions, Majorana fermions
- sheet 12: quantization of the Dirac equation
- sheet 13: classical scattering from a hard sphere, scattering from a central potential, resonant scattering
- sheet 14: scattering on a spherical potential well, 1/r
^{2}scattering potential

## Syllabus / Lectures

**week 1**: Concepts of quantum mechanics, limitations and advanced concepts, distinguishable vs. identical particles**week 2**: Fock space, creation and annihilation operators, real and momentum space operators**week 3**: Single- and two-particle operators, spinful fermions**week 4**: Weakly interacting Bose gases — from Bose-Einstein condensation to superfluidity**week 5**: Bogoluibov transformation, dynamics of fields, classical electrodynamics**week 6**: Interaction of light and matter**week 7**: Towards relativistic quantum mechanics — Einstein's theory of special relativity**week 8**: Lorentz-invariant electromagnetism, relativistic mechanics, Klein-Gordon equation**week 9**: Dirac equation**week 10**: electron spin and magnetic moment**week 11**: relativistic theory of the hydrogen atom, interpretation and quantization of the Dirac equation**week 12**: scattering theory: introduction, differential cross section, scattering states, partial wave method**week 13**: Lippmann-Schwinger equation, Green's function, Born approximation**week 14**: inelastic scattering, quantum information and entanglement**week 15**: entanglement and quantum computing

## Literature

- Franz Schwabl, Advanced Quantum Mechanics (Springer)

Uni-Bibliothek, Studierendenbibliothek Physik - R. Shankar, Principles of Quantum Mechanics (Springer)

Uni-Bibliothek, Studierendenbibliothek Physik - Albert Messiah, Quantum Mechanics Vol. 2 (North Holland)

Uni-Bibliothek, Studierendenbibliothek Physik - J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley)
- Scott Aaronson, Quantum Computing since Democritus (Cambridge University Press, 2013)
- M. Nielsen and I. Chaung, Quantum Computation and Quantum Information (Cambridge University Press)

Uni-Bibliothek, Studierendenbibliothek Physik - N. David Mermin, Quantum Computer Science (Cambridge University Press)

Studierendenbibliothek Physik

**Further general textbooks**

**Quantum information textbooks**

## Written exams

Written exam: Thursday,**February 26th, 2015**| 14:30 - 17:30 | HS I

Please keep in mind to sign up via

**KLIPS**no later than Tuesday, February 17th, 2015.

Retry exam: Tuesday,

**March 31st, 2015**| 13:00 - 16:00 | HS III

Please keep in mind to sign up via

**KLIPS**no later than Friday, March 20th, 2015 (even if you participated in the first written exam).

## Mailing-List

We have created a mailing list for this lecture, which will be used to send out further information regarding the lectures, exercise classes, and homework assignments.We ask all students to sign up for this mailing list.