Units

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Sample subject outline - Semester 1 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

Quantum mechanics is at the forefront in developing comprehensive physical understanding of our world, including natural links between macro- and micro-processes practically in all areas of modern physics, such as elementary particles, astrophysics, optics, lasers and spectroscopy, condensed matter physics, electronic devices and electronic engineering, nuclear physics, etc. Therefore, quantum theory is one of the most important and fundamental theories in physics, which has a tremendous impact on modern science and technology.

This unit is offered at the Honours level for students who wish to build on their knowledge in quantum mechanics obtained during their undergraduate studies. The unit will provide an essential platform for further studies and theoretical and experimental research in all areas that require knowledge of modern quantum theory. The unit is one of the essential and concluding units in your education in the physics major/co-major.

Aims

The main aim of the this unit is to develop a systematic knowledge of one of the most challenging and important topics in modern physics - quantum mechanical theory. You will learn the general mathematical formalism of QM and analytic techniques applicable to a wide range of QM problems.

Objectives

On successful completion of this unit, you will:

1. Be able to apply modern mathematical approaches and methods of quantum mechanics to particular problems of quantum theory and related areas.
2. Understand main concepts of non-relativistic quantum theory and its mathematical methods of analysis.
3. Develop general skills in problem solving, that will be applicable to various areas of pure and applied physics.
4. Develop an understanding of the relationships between the non-relativistic quantum theory and other areas of physics and engineering.

Content

Brief review of operators in quantum mechanics, wave functions, and the Dirac notation.
Matrix representation of operators and wavefunctions.
Basis sets; unitary transformations; projection and closure operators.
Representations and transitions between representations.
Observables. Complete sets of commuting observables.
Coordinate and momentum representations and observables. The R and P operators.
Tensor product of state spaces. Physical meaning of a tensor product state.
Measurements in quantum mechanics.
Properties of exponential operators: Glauber's formula; unitary transformations; Baker-Campbell-Hausdorff theorem.
Harmonic oscillator: generating function; raising and lowering operators.
Quantum rotator; spherical harmonics.
Hydrogen atom: derivation of radial and angular parts of the wavefunctions.
General theory of angular momentum. Universal matrices for the angular momentum operators.
Addition of angular momenta; spin-orbit interaction.
Density operator and the density matrix; evolution of DM; relationship between DM and physical observables.
General study of two-level systems; transition probability; Rabi theory (if time permits).
Time evolution operators and interaction representation.
Perturbation theory: higher-order stationary PT and time-dependent PT.
Magnetic field in quantum mechanics; vector potential; gauges (if time permits).

Approaches to Teaching and Learning

This unit will be given as a series of ~15 two-hour lectures. Students will also be expected to devote considerable time to individual study. This includes working with the textbook, solving practise problems, completing tutorial problem sets, and reading selected research papers from the field of physics.

Strong emphasis will be placed on tutorials and practise problems in order to develop problem-solving skills and ability to confidently use mathematical methods of quantum mechanics. Feedback will be provided to you on a continuous basis throughout the semester. Comprehensive lecture notes will be available on the BlackBoard web site.

Assessment

The assessment structure will reflect the emphasis of this unit on the general QM theory. The assessment will test your mastery of the problem-solving skills and analytic techniques presented in lectures.You will receive oral feedback from the Unit Coordinator following each Tutorial set and the mid-semester exam. You are also encouraged to contact the Unit Coordinator if you would like to discuss your progress and options for further learning.

Assessment name: Problem Solving Task
Description: (Formative and summative) - Tutorial Problems.
Relates to objectives: 1 to 3.
Weight: 35%
Internal or external: Internal
Group or individual: Individual
Due date: Weekly/Fortnightly

Assessment name: Examination (Theory)
Description: (Formative and summative) - Progress Examination
Relates to objectives: 1 to 3.
Weight: 35%
Internal or external: Internal
Group or individual: Individual
Due date: Approximately Week 8

Assessment name: Problem Solving Task
Description: (Summative) -Major assignment: Solution and discussion of Challenge Problems
Relates to objectives: 1 to 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Examination Period

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

Prescribed Text:

1. Cohen-Tannoudji C, Diu B & Laloe F (1977) Quantum Mechanics, 2 volumes, New York: J Wiley & Sons

Other Recommended Texts:

1. Merzbacher E (2000) Quantum Mechanics, John Wiley

2. Tamvakis K (2005) Problems and Solutions in Quantum Mechanics, Cambridge Univ. Press

3. Gol'dman II & Krivchenkov VD (2006) Problems in Quantum Mechanics, Dover Pubs.

Risk assessment statement

There are no out of the ordinary risks associated with this unit.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 17-Oct-2012