PHYSICS 7544 - Quantum Mechanics B
North Terrace Campus - Semester 2 - 2018
General Course Information
Course Code PHYSICS 7544 Course Quantum Mechanics B Coordinating Unit School of Physical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 4 hours per week Available for Study Abroad and Exchange Y Prerequisites PHYSICS 3542 or PHYSICS 7542, MATHS 2101 or MATHS 2201, MATHS 2102 or MATHS 2202 Incompatible PHYSICS 3022 Assumed Knowledge PHYSICS 2532 Course Description This course will introduce Dirac's bra-ket formulation of quantum mechanics and make students familiar with various approximation methods applied to atomic, nuclear and solid-state physics, and to scattering.
Content will include:
Dirac's formulation of quantum mechanics: kets and bras, quantum oscillator, angular momentum, measurement, Bell's inequality, generalised Uncertainty Principle, connection with wave and matrix mechanics. Time-independent and time-dependent perturbation theory, Schrodinger, Heisenberg and Interaction pictures, radiative transitions. Identical particles, atoms, exchange forces, periodic systems, energy bands in solids. Symmetries, translations in space and time, parity and time reversal, rotations and angular momentum, addition of angular momenta, fine structure of Hydrogen, L-S and j-j coupling in atoms and nuclei. Hartree-Fock and Thomas-Fermi approximations, variational and WKB methods. Scattering: Born approximation, S-matrix, partial waves.
Course Coordinator: Professor Anthony Thomas
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
1. develop a knowledge and understanding of the concept that quantum states live in a vector space;
2. develop a knowledge and understanding of the meaning of measurement;
3. relate this abstract formulation to wave and matrix mechanics;
4. develop a knowledge and understanding of perturbation theory, level splitting, and radiative transitions;
5. develop a knowledge and understanding of the relation between conservation laws and symmetries;
6. develop a knowledge and understanding of the role of angular momentum in atomic and nuclear physics;
7. develop a knowledge and understanding of the scattering matrix and partial wave analysis;
8. solve quantum mechanics problems;
9. use the tools, methodologies, language and conventions of physics to test and communicate ideas and explanations
10. integrate several components of the course in the context of a new situation (unique to postgraduate coursework).
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
1-7 Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
1-10 Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
8,9 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
1-10 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
This course will require ready access to the following texts and other resources:
Griffiths, D. J., Introduction to Quantum Mechanics, 2nd Edition (Pearson Prentice Hall, Upper Saddle River, NJ, 2005).
Sakurai, J.J. and Napolitano, J., Modern Quantum Mechanics, 2nd Edition (Pearson, Addison-Wesley, San Francisco, 2011)
Learning & Teaching Activities
Learning & Teaching Modes
Students are introduced to course content through lecture and independent reading. They develop their understanding through discussion, independent and group problem solving and completing assignments.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
A full-time student should expect to spend, on average, a total of 48 hours per week on their studies. This includes the formal contact time required for the course (e.g. lectures: 3 hours/week, workshops: 1 hour/week, practicals: 3 hours/fortnight), as well as non-contact time (e.g. reading and revision). For a 3-unit course, the expected workload would be, on average, 12 hours per week.
To complete their studies successfully, students are expected to attend all scheduled lectures, workshops and compulsory practical classes, as well as commit additional time to individual study, group study and the completion of assessment tasks. For a student to satisfactorily complete the academic requirements of a typical 3-unit course, a minimum TOTAL time commitment of 12 hours per week is expected (i.e. contact PLUS non-contact time). In addition, students should expect to study for one week of the two-week mid-semester break, as well as during swot week and the examination period.
Students who wish to excel and students whose background preparation for a course is poor should expect to commit additional time to that described above.
Learning Activities Summary
Ø Dirac's Quantum Mechanics
- Abstract ket vectors, dual bra-vector space and Dirac adjoint, Dirac operators, Schrödinger equation for kets
- Overlap amplitudes , measurement, polarisation and spin states, "collapse of the wave function"
- Hermitian and unitary operators, compatible observables, orthonormal ket basis, matrix elements
- Dirac ladder operators for the oscillator and for angular momentum
- Continuous eigenvalues, position and momentum wave functions as overlap amplitudes, relation to Fourier analysis
- Ehrenfest's theorem, generalised Heisenberg Uncertainty Principle, time-energy uncertainty
- Einstein-Podolsky-Rosen paradox, Bell's inequality, experimental evidence against hidden variables
Ø Time-Independent Perturbation Theory
- Non-degenerate theory, e.g. distorted square well, anharmonic oscillator
- Degenerate perturbation theory, 3-D oscillator, H atom, e.g. Zeeman effect
- Time-dependent Phenomena
- Schrödinger, Heisenberg and Interaction pictures
- Time-evolution operator, perturbation series
- Time-dependent perturbation theory, Golden Rule, radiative transitions
- describe scattering using time-dependent perturbation theory
- derive the formula for the t-matrix
- relate the t-matrix to the differential cross section
- understand the role of unitarity
Ø Symmetries in Quantum Mechanics
- Symmetries and conservation laws, space and time translations
- Discrete symmetries, parity and time-reversal
- Rotations and angular momentum
- Addition of angular momenta, orbital angular momentum and spin
- Degeneracy in hydrogen
- L-S and j-j coupling in atoms and nuclei
Ø Approximation Methods
- variational and WKB methods
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment task Type of assessment Percentage of total assessment
Yes or No #
Objectives being assessed / achieved Tests Formative & Summative 40% NO 1 – 10 Written Examination Summative 60% YES (40%) 1 – 10
Assessment Related Requirements
To obtain a grade of Pass or better in this course, a student must attend the examination and achieve a result of 40% or better in the examination.
Failure to meet these requirements (or not achieving the minimum mark for each learning requirement) will result in a grade of Fail (F).
While this course is offered concurrently to undergraduate students, all postgraduate students are expected to perform at a higher level both qualitatively and quantitatively. To facilitate this, postgraduate students are required to address additional content in the tests and the examination within the same timeframe as undergraduate students.
Tests: (40% of total course grade)
These will be used during the semester to address understanding of and ability to use the course material and to provide students a benchmark for the progress in the course.
Written Examination: (60% of total course grade)
One 3 hour exam is used to assess the understanding of and ability to use the material. Within the 3 hours, postgraduate students are required to answer additional question(s) in comparison to the undergraduate exam.
Poor performance in tests may be partly redeemed in the final exam.
Submission of Assigned Work
Coversheets must be completed and attached to all submitted work. Coversheets can be obtained from the School Office (room G33 Physics). Work should be submitted via the assignment drop box at the School Office.
Extensions for Assessment Tasks
Extensions of deadlines for assessment tasks may be allowed for reasonable causes. Such situations would include compassionate and medical grounds of the severity that would justify the awarding of a supplementary examination. Evidence for the grounds must be provided when an extension is requested. Students are required to apply for an extension to the Course Coordinator before the assessment task is due. Extensions will not be provided on the grounds of poor prioritising of time. The assessment extension application form can be obtained from: http://www.sciences.adelaide.edu.au/current/
Penalty for Late submission of assessment tasks
Assessment tasks must be submitted by the stated deadlines. There will be a penalty for late submission of assessment tasks: the submitted work will be marked ‘without prejudice’ and 10% of the obtained mark will be deducted for each working day (or part of a day) that an assessment task is late, up to a maximum penalty of 50% of the mark attained. An examiner may elect not to accept any assessment task that a student wants to submit after that task has been marked and feedback provided to the rest of the class. This procedure does not apply to the MyUNI quizzes which must be completed before the deadlines.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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