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Quantum Mechanics, 6 credits
Kvantmekanik, 6 hp
TFFY54
Main field of study
Applied Physics PhysicsCourse level
Second cycleCourse type
Programme courseExaminer
Magnus BomanDirector of studies or equivalent
Magnus JohanssonEducation components
Preliminary scheduled hours: 62 hRecommended self-study hours: 98 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
- Physics and Nanotechnology
- 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
Modern physics, linear algebra and fourier transform.Intended learning outcomes
The purpose of the course is to give the student a deeper understanding of quantum mechanics and to further develop the students ability to solve quantum mechanical problems. Following the course, the student should be able to:
- derive results based on the postulates of quantum mechanics.
- use various representations of quantum mechanics.
- solve quantum mechanical problems that involve topics listed in the course content.
Course content
Historical background. Wave-particle dualism. Wave packets. The time-dependent Schrödinger equation. Probability current density. Expectation values. Hermitian operators. Time-independent Schrödinger equation.
Boundary conditions. Properties of eigenfunctions. General solution to the Schrödinger equation. Time evolution operator. The Dirac notation. State space. Adjoint operators. Unitary operators. Commutator.
Rigorous proof of the uncertainity principle. Heisenberg's matrix representation. Ehrenfest's theorem. The postulates of quantum mechanics.
Harmonic oscillator with operator method. Operators as generators of translation and rotation. Symmetries and conservation laws. Generalized angular momentum. Spherical harmonics. Pauli spin matrices. Spin dynamics.
Spherical symmetric potential. The hydrogen atom in magnetic fields. Spin-orbit term. Conceptual problems. Approximative methods: non-degenerate and degenerate perturbation theory; the variational method.
Teaching and working methods
The course is divided into lectures and lessons (problem solving sessions).
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Quantum dynamics; Relativistic quantum mechanics; Elementary particle physics.
Department
Institutionen för fysik, kemi och biologiDirector of Studies or equivalent
Magnus JohanssonExaminer
Magnus BomanCourse website and other links
Education components
Preliminary scheduled hours: 62 hRecommended self-study hours: 98 h
Course literature
B. H. Bransden and C. J. Joachain, Quantum Mechanics, second edition, Prentice Hall 2000.| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written examination | 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.
Course literature is preliminary.
B. H. Bransden and C. J. Joachain, Quantum Mechanics,
second edition, Prentice Hall 2000.
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) |
X
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X
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X
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TEN1
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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 |
X
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
X
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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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| 3.3 Communication in foreign languages |
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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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| 5.5 Presentation and evaluation of research or development projects |
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