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FYS3110 - Quantum mechanics

Facts about this course: Credits: 10 Level: Advanced course at bachelor's level Teaching semester: Every autumn semester Examination semester: Every autumn semester Language of instruction: English if requested by exchange students, otherwise Norwegian Administrated by: Department of Physics

Detailed course information - Current and previous semesters: Autumn 2012 Autumn 2011 Autumn 2010 Autumn 2009 Autumn 2008 Autumn 2007 Autumn 2006 Autumn 2005 Autumn 2004 Autumn 2003

Course content

Vectors of state and transformation theory. Heisenberg picture and Schrõdinger picture. Harmonic oscillator with ladder operators. Translation and rotation. Coordinate representation. Calculus of variations. Spherically symmetric potentials. Quantisation of angular momentum and Clebsch-Gordan coefficients. Spin 1/2 and Pauli equation. Atomic physics. Stationary and time independent perturbation theory. Emission and absorption of light.

Learning outcomes

The student should be able to:

• Master mathematical concepts as Hilbert space, hermitean and unitary operators, orthogonal set of functions and the Dirac delta fucntion.

• Reproduce and explain the fundamental postulates of quantum mechanics.

• Explain and use fluently the Dirac notation, and be able to translate this to the coordinate representation as well as the matrix representation.

• Compute measurement results and their probabilitites for pure quantum states.

• Compute the time development of an arbitrary (pure) quantum state, and know the concept of the Schrødinger and the Heisenberg picture.

• Describe in details and be able to treat mathematically fundamental quantum concepts such as observable, expectation value, superposition and uncertainty relations.

• Define and use symmetries to simplify operator diagonalization and classification of the energy spectrum.

• Reproduce how a harmonic oscillator can be solved with ladder operators, and be able to use the ladder operators in order to compute matrix elements.

• Reproduce in detail the quantization of angular momentum, and be able to use ladder operators to solve problems with centralsymmetric potentials.

• Treat spin-1/2 systems quantitatively and be able to construct and to compute properties of combined spin states using Clebsch+Gordan coefficients.

• Reproduce with a low level of details properties of the lowest eigenstates of the Hydrogen atom.

• Describe the connection between bosons/fermions and wave function symmetries and Slate determinants.

• Reproduce with a low level of details properties of some many particle quantum systems such as the electron structure of the atom and the energy levels of solids.

• Compute changes in the energy spectrum up to second order, and states up to first order, using stationary and timedependent perturbation theory.

• Prove the variational principle and use it for simple quantum mechanical systems.

• Use semiclassical approximation methods as WKB on simple systems.

• Be able to understand relevant articles about quantum mechanics in Physical journals.

Admission

Students at UiO must apply for courses in StudentWeb.

International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

Prerequisites

Formal prerequisites

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

One of these:

• Mathematics R1
• Mathematics (S1+S2)

And and in addition one of these:

• Mathematics (R1+R2)
• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies. Read more about special admission requirements.

Recommended prior knowledge

FYS-MEK1110 - Mechanics, FYS1120 - Electromagnetism, FYS2130 - Waves and oscillations, FYS2140 - Quantum physics, MAT1100 - Calculus, MAT1110 - Calculus and linear algebra and MAT1120 - Linear algebra.

Overlap

10 credits overlap against FYS201.

Teaching

The course extends over a full semester with 4 hours of lectures and 2 hours of problem solving per week. 11 compulsory exercises where at least 6 of them must be graded pass in order to attend the final exam.

Exam information

One written home exam exam (approx. 25% weight) and a final written exam, 4 hours, (approx. 75% weight). In addition 6 of the 11 compulsory exercisis must be graded pass in order to attend the final exam.

Exam resources

Textbook:D.J. Griffiths "Introduction to Quantum Mechanics", one written A4 page with notes (2 pages), K. Rottmann "Matematisk formelsamling" og approved calculator.

Assessment and grading

Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail. Read more about the grading system .

An external auditor regularly evaluates the academic quality of the course, including the form of exam used on the course.

Explanations and appeals

Students can request an explanation of their grades, and can also appeal against their grades or make a complaint about formal examination errors. Read more about explanations and appeals

Possibility of make-up exams and re-takes

You can usually resit an exam, but the conditions depend on whether you had a valid reason for absence from the regular exam. Read more about resitting an exam .

Exam options for students with special needs

Students may apply for access to alternative exam resources or exam forms on the basis of chronic illness and/or special needs that create a marked disadvantage to other students in the exam situation. Mothers who are breastfeeding may apply for extra time to complete the exam.

Evaluation of this course

Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. As a student at the University of Oslo you will therefore be asked to participate in various types of evaluation of our courses, facilities and services. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, in-depth evaluation of this course, a so called "periodic evaluation".

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