| TFYA28 | Quantum Dynamics, 6 ECTS credits. /Kvantdynamik/ |
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Prel. scheduled
hours: 64 |
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Area of Education: Science Subject area: Physics |
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| Advancement level
(G1, G2, A): A
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| Aim: The purpose of the course is that the student after having passed the examination should have obtained such knowledge that the ability to understand research literature written with a quantum mechanical language should haven strikingly increased. After finishing the course the student knows:
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Recommended preknowledge : A basic course in quantum mechanics including perturbation theory, A fundamental course in material physics is recommended but not absolutely necessary. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Organisation: The course is presented in seminars. About 85 per cent of these are lectures and 15 per cent are problem solving sessions. |
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| Course contents: Will be chosen by: Introduction and repetition. Wave packets and their distortion. Group and phase velocity and the condition for stationary phase. x-, p-, and N-representation. Change of bases. Closure. Partitioning of the unit operator and projection operators. Spectral decomposition of operators. Unitary operators and trace (Spur). The evolution operator and its time-evolution. Schrödinger, Heisenberg and Dirac (Interaction) picture. Time-dependent perturbation theory. Fermi's golden rule (Dirac). Density operator. Pure and mixed states. Ensemble average. Classical and quantum mechanical Louisville equation (Avon Neumann's equation). Gage invariance. Many particle systems. Coupling of several spin. Screening. Hartree equations. Slater determinant and permanent. Hartree-Fock equations. Orientation about the X-alfa-method and the Kohn-Sham-theory. Second quantization or occupation number formalism. Orientating examples like the tight-binding model, Hubbard model, spin models (Heisenberg-, Ising-, XY-). Spin waves and magnons. Example of coupling between different kinds of quasi particles. Introduction to relativistic quantum mechanics. The Pauli equation according to Feynman. Klein-Gordon, Dirac and Weyl equation. Klein's paradox. Introduction to the quantization of the electromagnetic (Maxwell-) field or the Klein-Gordon field. Something about coherent states. Something about "squeezed light". Something about measurement and the EPR-paradox. Bell's theorem and and the publication of Greenberger-Horne-Zeilinger (GHZ). Orientation about some actual notions within the theory for condensed matter like localization, mobility edges, superlattices, quasiperiodicity, non-linearity, solitons, "breathers", selfsimilarity, multifractality, ... . |
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| Course literature: Lecture notes that can be purchased. |
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| Examination: | ||||
| Hand-in exercises and oral presentation |
4 p |
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6 ECTS |
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| Examination might be in the form of a written examination on problem solving and theory. | ||||
Course language is Swedish/English. Department offering the course: IFM. Director of Studies: Leif Johansson Examiner: Rolf Riklund Link to the course homepage at the department Course Syllabus in Swedish |
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