## MAS348 |
## 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.

- Course organiser

Rainer Klages; office hours: Mon 13.30-14.30h, Thu 16.30-17.30h

- Official web pages
College course directory Maths UG Handbook - Timetable

time room lecture

Mon 16.00-17.00 Maths G2

lecture

Thu 15.00-16.00 Queen's bldg. FB1 (basement)

lecture

Fri 16.00-17.00 Physics PLG1

exercise class

Mon 15.00-16.00

Maths G2

note the change of rooms for Thu/Fri! - Exercise sheets
no. hand out

due to

model solutions

sheet 1

5/10

19/10

solution 1

sheet 2

19/10

2/11

solution 2

sheet 3

2/11

16/11

solution 3

sheet 4

16/11

30/11

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

- 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: - 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

- 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

- 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

- Applications of QT:
Motion in one
dimension - potential step, tunnel effect, different types of infinite
potential wells

- Angular momentum and
its quantisation:
Spherically symmetric potentials, eigenvalue equations, ladder
operators, Hydrogen atom

- Course assessment Total credit for this course will be based on the following components:
- Coursework (10%)
- Final written exam (90%)
- Literature 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:
- Alastair I. M. Rae, Quantum mechanics (The Institute of Physics, 2002), Chapters 1 - 5 (short account of quantum theory)
- Brian H. Bransden, Charles Jean Joachain, Quantum mechanics (Prentice Hall, 2000), Chapters 1 - 7 (more details)
- 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)
- 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)

- 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)

- H. Hameka, Introduction to quantum mechanics (Harper and Row, New York, 1967) (see p.1-9)
- J.G. Taylor, Quantum mechanics - An introduction (Allen and Unwin, 1970) (see Chapter 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)
- Alastair I. M. Rae, Quantum physics: illusion or reality? (Cambridge University Press, 1986) (see particularly Chapter 1)
- John Gribbin, In search of Schrödinger's cat (Corgi, 1985) (see particularly Parts 1 and 2)
- Further information

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).