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Quantum Dynamics, 6 credits
Kvantdynamik, 6 hp
TFYA28
Main field of study
Applied Physics PhysicsCourse level
Second cycleCourse type
Programme courseExaminer
Iryna YakimenkoDirector of studies or equivalent
Magnus JohanssonEducation components
Preliminary scheduled hours: 64 hRecommended self-study hours: 96 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Applied Physics, PhysicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Physics and Nanoscience, Master's Programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Materials Science and Nanotechnology, Master's programme
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Quantum Mechanics, Modern physicsIntended learning outcomes
The main aim of the course is to give an exposition of the advanced concepts of quantum mechanics such as time-dependent perturbation theory, theory of many-particle systems, scattering theory, quantization of electromagnetic field and elements of relativistic quantum theory. After studying this course students should know:
- how to solve problems using such tools as state vectors and evolution operators, Schrödinger, Heisenberg and Dirac picture, non-pure states and density matrices
- the theory behind second quantization and some basic many-body systems
- the elements of scattering theory, quantization of electromagnetic field and relativistic quantum theory
- I.I. Yakymenko, Lecture Notes in Quantum Dynamics
Course content
Introduction and repetition. Wave packets. Group and phase velocity x-, p-, and N-representation. Change of bases. Closure. Spectral decomposition of operators. Unitary operators and trace. The evolution operator and its time-evolution. Schrödinger, Heisenberg and Dirac pictures. Time-dependent perturbation theory. Fermi's golden rule. Density operator. Pure and mixed states. Addition of angular momentum. Many particle systems. Hartree equations. Hartree-Fock equations. Density functional theory and the Kohn-Sham equations. Transport in two-dimensional semiconductor heterostructures. Second quantization or occupation number formalism. Tight-binding model and Hubbard model Scattering theory. Quantization of electromagnetic field. Interaction of matter with the light.Introduction to relativistic quantum mechanics. Klein-Gordon and Dirac equations. EPR-paradox and Bell's theorems.
Teaching and working methods
The course presented in the form of big seminars with theory and solution of problems
Examination
UPG1 Hand-in exercises and oral presentation 6 credits U, 3, 4, 5 Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Relativistic Quantum Mechanics, Particle Physics
Department
Institutionen för fysik, kemi och biologiDirector of Studies or equivalent
Magnus JohanssonExaminer
Iryna YakimenkoCourse website and other links
http://www.ifm.liu.se/undergrad/fysikgtu/coursepage.html?selection=all&sort=kkEducation components
Preliminary scheduled hours: 64 h
Recommended self-study hours: 96 hCourse literature
Additional literature
Compendia
Other
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Hand-in exercises and oral presentation | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Compendia
I.I. Yakymenko, Lecture Notes in Quantum Dynamics
Other
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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X
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X
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UPG1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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UPG1
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| 3.3 Communication in foreign languages |
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X
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X
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UPG1
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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X
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UPG1
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| 5.5 Presentation and evaluation of research or development projects |
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X
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UPG1
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