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| TFFY58 | Quantum Dynamics, 4,5 p (sw) /Kvantdynamik/ Advancement level: D | |
| Aim: To give a suitable transition from the basic concepts that was treated in the course Quantum Mechanics to concepts that are used in modern research.Prerequisites: TFFY54 Quantum Mechanics. The course TFFY02 Mathematical Methods of Physics, TFFY70, TFFY73 Physics of Condensed Matter part I and II are recommended.Course organization: The course is given in the form of 64 h seminars. About three quarters of the total time are devoted to lectures on the basic theory and one quarter to related problem solving sessions.Course content: Will be chosen among: Introduction and repetition. Wave packets and their distorsion. Group and phase velocities and the condition for stationary phase. x- p- and N- representation. Exchange of bases. Closure. Division of the unit operator with projection operators. Spectral resolution of operators. Unitary operators and trace. Evolution operator and its integral equation. Schrödinger, Heisenberg and Dirac (interaction) picture. Time dependent perturbation theory. Fermiīs golden rule (Dirac). Density matrix. Pure and mixed states. Ensemble averagdes. Quantum mechanical von Neumann equation and classical Liouville equation. Gaugeinvarians. Many particle systems. Something about coupling of several spins. Variational theory. Screening. Hartree equations. Slater determinant and permanent. Hartree-Fock equations. Orientation about the X-alpha-method and Kohn-Sham theory. Second quantization or occupation number formalism. Applied examples like the tight-binding model, the Hubbard model, spin-models (Heisenberg, Ising-, XY-). Spinnwaves and magnons. Example of coupling between different quasiparticles. Introduction to relativistic quantum mechanics. Pauli equation according to Feynman. Klein-Gordon, Dirac, and Weyl equation. Klein paradox. Something about quantization of the electromagnetic (Maxwell) field and the Klein-Gordon field. Something about coherent states. Something about squeezed states. Something about measurement and the EPR-paradox. Bellīs Theorem and the Greenberger-Horne- Zeilinger (GHZ) paper. Orientation about some topics of current interest like: localization, mobility edges, superlattices, quasiperiodicity, nonlinearity, solitons, breathers, selfsimilarity, multifractality,... . ... .Course literature: Lecture notes sold by Linus and Linnéa AB. | ||
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