From Classical Dynamics to Quantum Theory

Course Material Fall 2007

This is a new course that replaces the previous MAS217 Quantum Theory. Students who have already taken MAS217 are not allowed to register for this module.
  1. Course organiser
    Rainer Klages; office hours: Mon 13.30-14.30h, Thu 16.30-17.30h

  2. Official web pages
    College course directory
    Maths UG Handbook

  3. Timetable

    time room
    Mon 16.00-17.00 Maths G2
    Thu 15.00-16.00 Queen's bldg. FB1 (basement)
    Fri 16.00-17.00 Physics PLG1
    exercise class 
    Mon 15.00-16.00
    Maths G2

    note the change of rooms for Thu/Fri!

  4. Exercise sheets
    no.  hand out 
     due to
     model solutions
    sheet 1
    solution 1
    sheet 2
    solution 2
    sheet 3
    solution 3
    sheet 4
    solution 4
    sheet 5 30/11
    13/12 (Thu!)
    solution 5

    note: there are no exercise classes on 24/09, 8/10 and in the midterm week on 5/11

  5. Lecture regulations
  6. Students are expected to attend every lecture. Registers of attendance will be taken in lectures on a random basis.

  7. Coursework regulations
    Coursework will be handed out in the Friday lecture. You can also find it under the links above. The corresponding exercise classes will take place on the ensuing Mondays except on 8/10 and on 5/11.
    Your solutions must be handed in at the beginning of the lectures shown in the table above. Late work will not receive a mark. Copied work will be penalized.
    Please note: Not all of your coursework will be marked. Instead, I will mark a representative subset of questions. Usually I will mark around 30-50% of all questions and then scale the total mark of your coursework solutions according to the maximum of 100 marks. The questions I chose will be indicated on the model sulutions, which are available under the links above, by circled m's. Marked coursework will be given back to you in the lectures.
    Important: For your final mark, all 5 coursework sheets will count. Students failing to hand in at least 3 coursework solutions will be de-registered from this course. A mark of below 10 points constitutes a non-serious coursework submission.

    If you miss handing in a coursework for a serious reason, you should fill in a copy of the Missed In-Term Assessment Report Form (available from the web or from the Undergraduate Studies Handbook) and give it to the Pastoral Tutor Prof. Rosemary A. Bailey.

  8. Final exam
    The following topics are intended as a preliminary list of objectives to be mastered in order to be reasonably sure of passing the examination in Quantum Theory with a reasonable grade:
    1. Classical Hamiltonian mechanics: Hamiltonian, Newton's and Hamilton's equations, Poisson bracket and its properties, rate of change of dynamical variables, conserved dynamical variables, angular momentum, graphical discussion of possible types of motion of point particles in given potentials
    2. Rise of quantum mechanics: Definition of different types of Schroedinger equations, wave functions and their properties, boundary conditions, stationary states, quantisation rules classical to quantum theory
    3. Mathematical foundations of QT: Vector spaces, scalar product and its properties, orthogonal and orthonormal basis, linear operators and their properties, Hermitian conjugate, Hermitian operators, properties of eigenvalues and eigenfunctions of Hermitian operators, expectation and standard deviation for operators, commutators and their properties, mathematical statement of uncertainty principle
    4. Applications of QT: Motion in one dimension - potential step, tunnel effect, different types of infinite potential wells
    5. Angular momentum and its quantisation: Spherically symmetric potentials, eigenvalue equations, ladder operators, Hydrogen atom
    The final exam will take place probably some time in May 2008. Its duration will be two hours. The rubric will state: You should attempt all questions. Marks awarded are shown next to the questions. Calculators are NOT permitted in this examination.
    Please note: I will not hand out model solutions for past exams. All solutions to previous exams are either in your lecture notes or in your coursework solutions. However, I will be available for answering specific questions during my office hours.
    Previous exam papers you can find here (see link under Quantum Theory).

  9. Course assessment
  10. Total credit for this course will be based on the following components:
    1. Coursework (10%)
    2. Final written exam (90%)
    There is no midterm test for this course.

  11. Literature
  12. All of the following books are available in the main library. Please note that the first three books have been put into the short loan collection:
    1. Alastair I. M. Rae, Quantum mechanics (The Institute of Physics, 2002), Chapters 1 - 5 (short account of quantum theory)
    2. Brian H. Bransden, Charles Jean Joachain, Quantum mechanics (Prentice Hall, 2000), Chapters 1 - 7 (more details)
    3. Michael A. Morrison, Understanding Quantum Physics: A User's Manual (Prentice Hall, 1990) (recommended if you have trouble with the material presented in the lectures and need a very detailed presentation)
    For the first 2 weeks of this course dealing with classical mechanics, the following books might be helpful:
    1. R.P. Feynman, R.B. Leighton, M. Sands, The Feynman lectures on physics, Vol. 1 (Addison-Wesley, Reading, Mass., 1977) (if you are not familiar with Newton's Laws see Section 9.1-9.5 and 10.1)
    2. H.C. Ohanian, Physics (W.W. Norton and Co., New York) (Section 5.1-5.5 for a very elementary introduction to Newton's Laws and Newtonian mechanics)
    3. H. Hameka, Introduction to quantum mechanics (Harper and Row, New York, 1967) (see p.1-9)
    4. J.G. Taylor, Quantum mechanics - An introduction (Allen and Unwin, 1970) (see Chapter 1)
    If you are interested in the conceptual background of quantum mechanics (history of this theory, philosophical implications, etc.), as an introduction you may look into the following books:
    1. J. E. Baggott, The meaning of quantum theory: a guide for students of chemistry and physics (Oxford University Press, 1992) (particularly p.1-55)
    2. Alastair I. M. Rae, Quantum physics: illusion or reality? (Cambridge University Press, 1986) (see particularly Chapter 1)
    3. John Gribbin, In search of Schrödinger's cat (Corgi, 1985) (see particularly Parts 1 and 2)

    There will be no lecture notes, however, here is a table of contents of the previous lecture.
    Note: Preknowlegde in physics would be helpful but is not necessary. All the physics you need to know will be explained in this course.

  13. Further information
    1. course information sheet
    2. key objectives and exam rubric
    3. quantum theory at Queen Mary
last modified: September 24th, 2007