Print syllabusAdvanced Graduate Quantum Mechanics
General data
| Course ID: | 1100-SZD-AGQM |
| Erasmus code / ISCED: | (unknown) / (unknown) |
| Course title: | Advanced Graduate Quantum Mechanics |
| Name in Polish: | Advanced Graduate Quantum Mechanics |
| Organizational unit: | Faculty of Physics |
| Course groups: |
(in Polish) Przedmioty do wyboru dla doktorantów; |
| Course homepage: | https://www.fuw.edu.pl/~byczuk/ |
| ECTS credit allocation (and other scores): |
6.00
|
| Language: | English |
| Main fields of studies for MISMaP: | physics |
| Prerequisites (description): | Quantum mechanics, classical electrodynamics, statistical physics, or equivalent ones, and basic corses in mathematics and mathematical analysis. |
| Mode: | Blended learning |
| Short description: |
The corse discusses various selected topics in quantum mechanics typically not included in basic courses. The emphasis is put on physical aspects not on a mathematical rigor. |
| Full description: |
1. Symmetry in quantum mechanics - symmetry operations - T, P, C symmetries - translational symmetry - rotational symmetry - conservation laws - gauge symmetry 2. Symmetry breaking in quantum mechanics - crystal lattice and symmetry breaking - phonons as Goldstone modes - superconductors, Anderson-Higgs modes and massive photons 3. Topology in quantum mechanics - Aharonov-Bohm effect - Landau levels and integer quantum Hall effect - Berry phase - topological insulators - quantum number fractionalization - SH polymer model - zero modes and Majorana quasiparticles 4. Scattering and resonant states - formal theory of scattering - T and S matrix, symmetry, unitarity - poles and branch cuts of S-matrix - understanding of resonant states 5. Application of Rigged Hilbert spaces in quantum mechanics - needs to extend the Hilbert spaces for unbounded, continuous operators - spaces of physical, trial wave functions - linear and anti linear distribution spaces - rigorous interpretations of bra < | and ket | > Dirac states - examples: free particles, resonant Gamow state 6. Different formulations of quantum mechanics - Schroedinger formulation - Heisenberg formulation - density matrix, pure and mixed states - resolvent - phase space formulation, Wigner quasi probability function - path integrals - Bohm theory - Fock space and occupation number formalism 7. Measurement and interpretation problems in quantum mechanics - Bohr - von Neumann - Everett - Bohm 8. Entanglement states - concept of entanglement, Bell states - EPR paradox and its discussion - no-cloning theorem - teleportation algorithm - Bell inequalities and experimental verifications - progress and prospects in quantum computing 9. Quantum-classical correspondence - signature of chaos in quantum systems - random-matrix theory - level statistics (*) In case of time shortage last topics will be canceled. |
| Bibliography: |
Different book's chapters and review articles provided during the course. |
| Learning outcomes: |
A student should know about various extensions and applications of quantum mechanics in modern physical sciences. A student should be able to solve basic problems illustrating discussed topics. |
| Assessment methods and assessment criteria: |
written colloquium and written and oral exams |
Classes in period "Summer semester 2023/24" (in progress)
| Time span: | 2024-02-19 - 2024-06-16 |
 
MO TU WYK
W CW
TH FR |
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
| Coordinators: | Krzysztof Byczuk | |
| Group instructors: | Krzysztof Byczuk | |
| Students list: | (inaccessible to you) | |
| Examination: | Pass/fail |
Copyright by University of Warsaw.
