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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TIF290 - Quantum mechanics
Kvantmekanik
 
Syllabus adopted 2019-02-14 by Head of Programme (or corresponding)
Owner: MPPHS
4,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS


Teaching language: English
Application code: 85118
Open for exchange students: Yes
Block schedule: B

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Examination 4,5c Grading: TH   4,5c   Contact examiner,  Contact examiner,  Contact examiner

In programs

MPPHS PHYSICS, MSC PROGR, Year 1 (compulsory)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)

Examiner:

Philippe Tassin

  Go to Course Homepage


Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Introductory courses in: linear algebra, complex calculus, differential equations, analytical mechanics, electromagnetism, and quantum mechanics.

Aim

As a continuation of the introductory quantum mechanics courses, this course aims at providing the students with a firm, deeper knowledge of nonrelativistic quantum mechanics, at demonstrating the power of quantum mechanics to describe microscopic phenomena, and at introducing the students to contemporary applications. The course will start with a brief review of the foundations of quantum mechanics and will then continue with powerful techniques to study the behaviour of single-particle or few-particle quantum systems. The course will gradually move towards more complex systems, eventually leading to second quantization and a description of spontaneous and stimulated emission of light. These concepts will be illustrated by examples from modern technology, including a guest lecture on quantum information and quantum computing. In this way, the course will help preparing the students for courses in, for example, condensed matter physics, quantum field theory, or spectroscopy.

Learning outcomes (after completion of the course the student should be able to)

- Explain the basic principles of quantum mechanics;
- Describe the dynamics of quantum-mechanical systems in the Schrödinger, Heisenberg, and interaction pictures;
- Explain the correspondence principle and how classical mechanics relates to quantum mechanics;
- Use the WKB approximation;
- Apply scattering theory to calculate the cross section of quantum particles interacting with a potential, another particle, or a crystal;
- Describe how to model particles in a magnetic field and use this to explain the Zeeman and the Aharonov-Bohm effect;
- Understand the concept of the density operator and apply it to describe ensembles and open systems;
- Describe and explain second quantization and apply it to lattice vibrations (phonons) and the electromagnetic field (photons);
- Use the concepts developed in the course to describe the phenomena of spontaneous and stimulated emission;
- Discuss the basic principles of quantum information and quantum computing;
- Read scientific literature on the above topics.

Content

- Brief review of Dirac notation; noncommuting observables; representations
- Quantum dynamics: the Schrödinger, Heisenberg, and interaction pictures
- Correspondence principle, Ehrenfest's theorem; hidden variables, Bell inequalities
- WKB approximation
- Scattering theory
- Charged particles in a magnetic field, Zeeman effect, Aharonov-Bohm effect
- Density operator, pure and mixed states, ensembles and open systems
- Second quantization
- Radiative transitions; spontaneous and stimulated emission; Rabi oscillations
- Quantum information; entanglement; no-clone theorem; quantum computing

Organisation

The course will consist of lectures, problem-solving sessions, and guest lectures. Attendance at the guest lectures is compulsory.

Literature

- Modern Quantum Mechanics, Revised Edition by J. J. Sakurai and J. Napolitano (Addison-Wesley);
- Lecture notes from Ben Simons' Advanced Quantum Mechanics course (University of Cambridge);
- Handouts provided by the lecturer

Examination including compulsory elements

Students will be examined by way of compulsory assignments to be handed in during the course and a compulsory oral exam at the end of the course. To receive any passing grade (3, 4, or 5), at least that grade must be earned both on the assignments and on the oral exam.


Published: Wed 26 Feb 2020.