MACQUARIE UNIVERSITY Department of Physics Division of ICS PHYS304 Quantum Physics II (2005) Unit Outline This is a three credit point unit intended to further develop the study of quantum mechanics. The material presented follows, in spirit if not in actual detail, the development of the subject pioneered by Feynman in The Feynman Lectures on Physics with an emphasis on the use of the Dirac formalism, and adopts the perspective of the modern views of quantum information theory. The unit addresses some of the philosophical underpinnings of the subject and its impact on our view of the nature of the physical world, the mathematical language in which the ideas of quantum mechanics are expressed, and applications of these ideas to various areas of modern physics. LECTURERS Dr James Cresser E7A208 9850 8913 jcresser@physics.mq.edu.au (Unit convenor) Prof. Jason Twamley. TEXTS There is no prescribed text for this unit. Some of the texts worth consulting are listed below. J. J. Sakurai Modern Quantum Mechanics. J. S. Townsend A Modern Approach to Quantum Mechanics. C. Cohen-Tannoudji, B. Diu, and Quantum Mechanics Two Volumes F. Laloë E. Merzbacher Quantum Mechanics A. Messiah Quantum Mechanics Two Volumes A. Das and A. C. Melissinos Quantum Mechanics, a Modern Introduction. R. P. Feynman, R. B. Leighton, and The Feynman Lectures on Physics, Vol III M. Sands R. L. Liboff Introductory Quantum Mechanics. P. A. M. Dirac The Principles of Quantum Mechanics. The first five books are highly recommended reference texts. Dirac s book was once considered the bible on the subject, and is still worth reading for the thoroughness of its discussion, but the more modern texts such as that by Cohen-Tannoudji et al are recommended if you are looking for a more up-to-date perspective. Web-based Material From time to time, material such as assignments, assignment solutions, additional lecture material and so on for Dr Cresser s half of the unit will be made available on the web at http://www.physics.mq.edu.au/ jcresser and follow the links to Phys304.
ASSESSMENT Requirements for Completion of Course As required by Academic Senate these requirements are stated as 1. Attendance and satisfactory performance in the examination; and 2. An aggregate standard number grade (SNG) corresponding to a pass (P). (PC grade corresponds to a lower SNG) Assignments 30% Final Exam 70% (3 hours plus 10 minutes reading time) The use of electronic calculators in the examination for this unit is permitted, but in accordance with Division policy, is restricted to the use of models that do not have a full alphabet on the keyboard. The use of any calculator is of course encouraged at all other times, and any inconvenience arising from the restriction during examinations is regretted. Assignments Assignments will be given out on 3 rd August, 17 th August, 31 th August and 14 th September in the first half of the semester, and approximately every two weeks thereafter. The assignments are to be returned a week later. There is no minimum number of assignments required to be handed in, but of course, if you do not attempt the assignments, you will miss out on 30% of your final grade, and you will also miss out on valuable problem-solving experience. You will learn as much from the assignments as from lectures themselves. Students who have entered this unit with a waiver of prerequisites must hand in their assignments as required. No further concessions or assistance can be offered to these students if they fail to work as expected. UNIT CONTENT Below is a summary of the topics to be covered. The material follows on from where PHYS301 left off. Not all topics will be covered to the same depth of detail, and there may be some variation from this list from time to time. First Half Semester (Dr J Cresser) 1. Introduction and review of PHYS301 material. 2. Further development of operators in quantum mechanics: sums and products of operators, Dirac ket-bra notation, unitary operators, projection operators, functions of operators. 3. Continuous eigenstates, Dirac delta function normalization. 4. Compatible and incompatible measurements, commutators, the Heisenberg uncertainty principle. 5. Time evolution revisited, space displacement. 6. Symmetry in quantum mechanics: operations on quantum system, symmetry operations and conservation laws in quantum mechanics.
7. Canonical quantization (very briefly). 8. The position and momentum representations. Schrödinger s wave equation. 9. The simple harmonic oscillator in position representation. 10. The simple harmonic oscillator operator solution. Second Half Semester (Prof J Twamley content of this half subject to change) 1. Generalization to three dimensions. 2. Angular momentum in quantum mechanics: angular momentum operators, orbital and spin angular momentum, spherical harmonics. 3. State space for combined systems. 4. Identical particles: boson and fermion many particle states. 5. Semiclassical treatment of electromagnetic field in quantum mechanics, the minimal coupling Hamiltonian, dipole approximation, Rabi oscillations. 6. Quantization of the electromagnetic field in a single mode cavity. 7. Transition probabilities; time-dependent perturbation theory, stimulated emission and absorption. 8. Time independent perturbation theory, the Stark effect, van der Waals forces. OTHER IMPORTANT INFORMATION Generic Skills Reading, interpreting and understanding reading resources; Numerical, quantitative and mathematical skills assignment problems, linear algebra in lecture content and problems; Problem solving assignments; Creativity problem solving approach; Developing an appreciation of a new view of the nature of the physical world. Student Liaison Committee The Physics Department values quality teaching and engages in periodic student evaluations of its units, external reviews of its programs and course units, and seeks formal feedback from students via focus groups and the Student Liaison Committee (SLC). Please consider being a member of this committee, which meets once during the semester (lunch provided), with the purpose of improving teaching via student feedback. The class will be asked to nominate two students as representatives for the PHYS304 unit on the student liaison committee. This nomination process will be conducted during lectures and the lecturer will forward the names to the Head of Department. Summaries of the discussion will be reported to Physics Dept meetings where decisions on actions will be taken. These summaries will also be reported to the SLC as well as being posted. The policy and procedure of this committee are still under development. Plagiarism The University Senate approved definition and guidelines for avoiding plagiarism are attached.
Special Consideration Students who are prevented by unavoidable disruption from completing any of the work required to complete a unit should report the circumstances in writing (supported by an original medical certificate or other proper evidence) to the Registrar s Office. The information supplied will then be referred to the Head of the Division in which the unit is offered, to take into account when assessing the student s performance (see Rule 9 of the Bachelor Degree Rules). Where students were prevented by unavoidable disruption from attending an examination or prior to or during an examination were affected by unavoidable disruption which they believe prejudiced their performance, they should report the circumstances in writing to the Registrar s Office. The report (supported by an original professional authority form or other proper evidence) should reach the Academic Program Section of the Registrar s Office as soon as possible after such examination, and in any case not later than the day following the final day of the examination period. The information supplied will then be referred to the Head of the Division in which the unit is offered who may, after considering the information, recommend that Academic Senate grant a special examination. J Cresser 1 st August2005
Plagiarism The Academic Senate in September 1992 adopted the following definition of plagiarism. Plagiarism involves using the work of another person and presenting it as one s own. Any of the following acts constitutes plagiarism unless the source of each quotation or piece of borrowed material is clearly acknowledged. 1. copying out part(s) of any document or audio-visual material (including computer-based material); 2. using or extracting another person s concepts, experimental results, or conclusions; 3. summarising another person s work; 4. in an assignment where there was collaborative preparatory work, submitting substantially the same final version of any material as another student. Encouraging or assisting another person to commit plagiarism is a form of improper collusion and may attract the same penalties which apply to plagiarism. Senate also approved a statement entitled The Dangers of Plagiarism and How to Avoid it which is as follows: The Dangers of Plagiarism and How to Avoid it The integrity of learning and scholarship depends on a code of conduct governing good practice and acceptable academic behaviour. One of the most important elements of good practice involves acknowledging carefully the people whose ideas we have used, borrowed or developed. All students and scholars are bound by these rules because all scholarly work depends in one way or another on the work of others. Therefore, there is nothing wrong in a student using the work of others as a basis for their own work, nor is it evidence of inadequacy on the student s part, provided they do not attempt to pass off someone else s work as their own. To maintain good academic practice, so that a student may be given credit for their own efforts, and so that their own contribution can be properly appreciated and evaluated, they should acknowledge their sources and they should always: 1. state clearly in the appropriate form where they found the material on which they have based their work, using the system of reference specified by the Division in which their assignment was set; 2. acknowledge the people whose concepts, experiments, or results the students have extracted, developed, or summarised, even if they put these ideas into their own words; 3. avoid excessive copying of passages by another author, even where the source is acknowledged. Find another form of words to show that the student has thought about the material and understood it, but stating clearly where they found the ideas. If a student uses the work of another person without clearly stating or acknowledging their source, the result is falsely claiming that material as their own work and committing an act of PLAGIARISM. This is a very serious violation of good practice and an offence for which a student will be penalised. A student will be guilty of plagiarism if they do any of the following in an assignment, or in any piece of work which is to be assessed, without clearly acknowledging their source(s) for each quotation or piece of borrowed material: 1. copy out part(s) of any document or audio-visual material, including computer-based material; 2. use or extract someone else s concepts or experimental results or conclusions, even if they put them in their own words; 3. copy out or take ideas from the work of another student, even if they put the borrowed material in their own words; 4. submit substantially the same final version of any material as a fellow student. On occasions, a student may be encouraged to prepare their work with someone else, but the final form of the assignment must be their own independent endeavour.