PHYSICS 7542 - Quantum Mechanics A
North Terrace Campus - Semester 1 - 2015
General Course Information
Course Code PHYSICS 7542 Course Quantum Mechanics A Coordinating Unit School of Physical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites PHYSICS 2510, MATHS 2101 or MATHS 2201, MATHS 2102 or MATHS 2202 Incompatible PHYSICS 3004, PHYSICS 3542 Assumed Knowledge PHYSICS 2532, PHYSICS 2534 Course Description This course develops concepts in quantum mechanics such that the behaviour of the physical universe can be understood from a fundamental point of view. It provides a basis for further study of quantum mechanics.
Content will include: Review of the Schrodinger equation, operators, eigenfunctions, compatible observables, infinite well in one and three dimensions, degeneracy; Fourier methods and momentum space; Hermiticity; scalar products of wave functions, completeness relations, matrix mechanics; harmonic oscillator in one and three dimensions; sudden approximation; central potentials, quantisation of angular momentum, separation of radial and anqular variables, spherical harmonics, hydroqen atom, spin.
Course Coordinator: Dr Rodney Crewther
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
1. show an understanding of wave mechanics in three dimensions;
2. describe the structure of the hydrogen atom and show an understanding of quantisation of angular momentum;
3. apply techniques such as Fourier methods and ladder operators for selected problems in quantum mechanics;
4. use the tools, methodologies, language and conventions of physics to test and communicate ideas and explanations;
5. use the tools, methodologies, language and conventions of physics to test and communicate ideas and explanation
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) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1-5 The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 1-5 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 3-5 Skills of a high order in interpersonal understanding, teamwork and communication. 4 A proficiency in the appropriate use of contemporary technologies. 3-4 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1-5
Required ResourcesGriffiths, D. J. (2005) Introduction to Quantum Mechanics 2nd ed. (Pearson Prentice Hall) http://academic.reed.edu/physics/faculty/griffiths.html
- Gasiorowicz, S. (2003) Quantum Physics 3rd ed. (Wiley),
- Bransden, B. H., and Joachain, C. J. (2000) Quantum Mechanics 2nd ed., (Pearson)
http://stellar.mit.edu/ Register free MIT “Touchstone” account, subject 8.05
MyUni: Teaching materials and course documentation will be posted on the MyUni website (http://myuni.adelaide.edu.au/).
Learning & Teaching Activities
Learning & Teaching Modes
- 2 Lectures of 1 hour each per week
- 2 Tutorials of 1 hour per 3 week period
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
A student enrolled in a 3 unit course, such as this, should expect to spend, on average 12 hours per week on the studies required. This includes both the formal contact time required to the course (e.g., lectures and practicals), as well as non-contact time (e.g., reading and revision).
Learning Activities Summary
Ø Level II Upgrade
- Wave vector, operators, expectation values, Schrödinger equation, separation of space and time variables, all done in three dimensions.
Ø Fourier Methods
- Fourier series for infinite square well, coefficients as overlap integrals, Fourier integral and inverse as limiting case, Parseval and convolution properties, Dirac delta function, extension to three dimensions.
- Quantum mechanics in momentum space: operators and Schrödinger equation, invariance of overlap integrals, wave-packet (group) velocity
Ø Formal Developments
- Differential operators: Hermitian adjoint, orthonormal eigenfunctions, Gram-Schmidt method for degenerate eigenvalues.
- Compatible observations, simultaneous eigenstates, 3-D square well (example).
- Vector space of wave functions, completeness, analogy with spanning a finite space, overlap amplitude as inner product (f,y), matrix representation, orthonormality for continuous eigenvalues.
Ø Harmonic Oscillator
- Ladder operators, energy eigenfunctions, expectation values via algebraic methods.
- Series solution (Frobenius) of 2nd order equation.
- Extension to three dimensions.
- Sudden approximation.
Ø Central Potentials and Angular Momentum
- Reduced mass, CM frame, orbital L in sphericals, connection between L2 and K.E.
- Quantisation of L, ladder operators, eigenvalues and eigenstates.
- Laplacian in sphericals, separation of r and q,j variables, radial equation with centrifugal barrier, separation of q and j with l = integer, spherical harmonics, parity.
- H-atom bound states: solution of radial equation (Frobenius), principal quantum number n, simultaneous eigenstates
with degeneracy 2n2, structure of periodic table.
- Spin angular momentum S, polarisations under rotations, total angular momentum; particle spin (examples); Stern-Gerlach experiment, sequential S-G experiments; spinors, Pauli matrices; level-splitting effects in H spectrum (qualitative).
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 Assignments, tests & online responses Formative & Summative 30 - 40% No 1 – 5 Exam Summative 60 - 70% No 1 – 4
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 projects and the examination within the same timeframe as undergraduate students.
Assignments, Tests and online responses
The mix of assignments and tests will be decided at the start of the semester by negotiation with students. A combination of on-line responses, tests and summative assignments 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 (40% of total course grade). Postgraduate students are required to complete additional assessment tasks within each assignment, test and online responses to demonstrate additional understanding of the course material, in particular the ability to integrate different course components in a novel context.
One 2-hour exam will be used to assess knowledge and understanding of and ability to use the material (60% of total course grade).
Poor performance in assignments and tests can be partially compensated by a higher weighting of the examination in the final assessment.
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) or from MyUNI. 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/
Late submission of assessments
If an extension is not applied for, or not granted then a penalty for late submission will apply. A penalty of 10% of the value of the assignment for each calendar day that is late (i.e. weekends count as 2 days), up to a maximum of 50% of the available marks will be applied. This means that an assignment that is 5 days or more late without an approved extension can only receive a maximum of 50% of the mark.
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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