PHYSICS 3544 - Quantum Mechanics III

North Terrace Campus - Semester 2 - 2019

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.

  • General Course Information
    Course Details
    Course Code PHYSICS 3544
    Course Quantum Mechanics III
    Coordinating Unit School of Physical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 4 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites PHYSICS 3542, 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 Staff

    Course Coordinator: Professor Anthony Thomas

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    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. elate 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
    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
    1-9
    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
    1-9
    Intercultural and ethical competency
    • adept at operating in other cultures
    • comfortable with different nationalities and social contexts
    • Able to determine and contribute to desirable social outcomes
    • demonstrated by study abroad or with an understanding of indigenous knowledges
    9
    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
    9
  • Learning Resources
    Required Resources

    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)

    Online Learning

    MyUni: Teaching materials and course documentation will be posted on the MyUni website (http://myuni.adelaide.edu.au/).

  • Learning & Teaching Activities
    Learning & Teaching Modes

    This course will be delivered by the following means:

    • Lectures 36 x 50-minute sessions with three sessions per week
    • Tutorials 11 x 50-minute sessions with one session per week
    Workload

    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

    The course content will include the following:

    Coursework Content

    • 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
    • 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
    • Scattering
      • 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
    • 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
    • Approximation Methods
      • variational method
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Assessment taskType of assessmentPercentage of total assessment for grading purposesHurdle (Yes/No)Outcomes being assessed
    Tests Formative & Summative 30-40% No 1 – 9
    Written Examination Summative 60-70% Yes (40%) 1 – 9
    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.

    Assessment Detail

    Tests: (30-40% 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: (60-70% of total course grade)
    One 3 hour exam is used to assess the understanding of and ability to use the material.

    Poor performance in tests may be partly redeemed in the final exam.

     

    Submission

    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 replacement 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.

    Course Grading

    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.

  • Student Feedback

    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.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

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