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| NFYD65 | Quantum Dynamics, 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 and Molecular Physics to concepts that are used in modern research.Prerequisites: Participation in NFYC58 Quantum Mechanics and Molecular Physics and NFYC52 Mathematical Methods of Physics 2.Supplementary courses: NFYD74 Elementary particle physicsCourse organization: The course is given in the form of seminars. About three quarters of the total time is devoted to lectures and one quarter to related problem solving sessions.Course content: Will be chosen among: Introduction and repetition. Dirac-formalism. Wave packets and their distortion. Group 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 pertubation theory. Fermi's golden rule (Dirac). Density matrix. Pure and mixed state. Ensemble averages. Quantum mechanical and classical Liouville equation. Gauge-invariance. Many-particle system. 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-). Spin-waves and magnons. Example of coupling between different quasiparticles. Introduction to relativistic quantum mechanics. The Pauli equation according to Feynman. The Klein-Gordon, Dirac, and Weyl equations. The Klein paradox. Quantization of the electromagnetic (Maxwell) field and the Klein-Gordon field. Coherent states and squeezed states. The measurement problem and the EPR-paradox. Bell's theorem and the Greenberger-Horne-Zeilinger (GHZ) paper. Orientation about some topics of current research interest in solid state theory.Course literature: Lecture notes sold by Linus and Linnea AB.Assessment: | ||
| Examination. The examination will be given in the form of homework problems. | ||
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