FYS4110 – Advanced Quantum Mechanics

Upon course completion the student will be able to:

• use the density-operator formalism and generalized measurement theory: compute reduced states via partial trace, evaluate expectation values, and model measurements using POVMs and Kraus/quantum-operation representations.
• analyze composite quantum systems and quantify entanglement: perform Schmidt decompositions, compute entanglement measures for simple states, and evaluate Bell/CHSH correlations and their quantum bounds.
• apply harmonic-oscillator methods and characterize nonclassical states: construct coherent and squeezed states using displacement/squeezing operators and compute quadrature uncertainties and photon-number statistics.
• employ phase-space and coherence-function methods: work with P-, Q-, and Wigner representations, compute basic quasiprobability distributions, and use first/second-order correlation functions to interpret coherence and photon statistics.
• use advanced formalisms relevant to modern quantum physics: set up coherent-state and spin path integrals, compute Berry phases for simple systems, and explain basic topological invariants (e.g., Chern number) at a conceptual/working level.
• formulate quantum field and many-body descriptions: quantize the electromagnetic field in modes, use second-quantized operators for bosons/fermions, and apply these ideas to representative model Hamiltonians.
• Model dissipation and measurement in open quantum systems: derive and solve simple Lindblad master equations, use quantum Langevin equations conceptually/operationally, and connect to noise spectra and input-output relations.
• apply the toolbox to canonical physical systems: analyze light-matter interaction (Jaynes-Cummings), spontaneous emission and photodetection, and core devices such as parametric amplifiers, lasers, and cavity/circuit QED systems (with optomechanics as an outlook).

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

• FYS2140 – Quantum Physics
• FYS3110 – Quantum Mechanics

The first lecture is mandatory. If you are unable to attend, the Department of Physics has to be informed no later than the same day (studieinfo@fys.uio.no), or else you will lose your place in the course.

The course is given for a full semester with 6 hours teaching per week, with a combination of frontal lectures (4 hours) and exercise sessions (2 hours).

A group project must be completed and approved before you can sit the final exam.

See rules for mandatory activities/assignments.

• Final oral exam which counts 100 % towards the final grade.

A group project must be approved before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: FYS9110 – Advanced Quantum Mechanics

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.