 
Summary: Title Assignment Seminar Mathematical Physics
E. van Groesen, UTwente (groesen@math.utwente.nl)
Autumn 2003
Organisation for ...nalising the course:
Each student has to ...nish three `groups'of assignments:
1. The general assignments about WKB as given by van Groesen (described below, to be handed
in electronically)
2. The general assignments about existence travelling waves by Van Gils (hand in withVan Gils)
3. A special assignment consisting of a more extensive exercise, to be chosen from a topic given by
Van Groesen, or Van Gils or Molenaar (ask them).
Assignments 1 and 2 have to be ...nished before 16 October.
Assignment 3 has to be ...nished before December 1.
General Assignments WKB (4 exercises)
The standard equation to be considered is:
@2
z u + k2
(z)u = 0: (1)
Physically u can be interpreted as the spacedependent part of the timeharmonic wave u(z) exp( i!t):
For general k(z) the general solution cannot be written down in elementary functions. Based on the
explicit solution for constant k, written in complex notation like
