NONLINEAR DYNAMICS: QUANTUM CHAOS  
        ----------------------------------------------------------- 

	Georgia Tech PHYS 7224			Spring semester 2002  
	Predrag Cvitanovic'

        Lecture 3:        12:05-13:25 Thu Jan 15 2002 in Howey S106


Semiclassical propagation
-------------------------

Hamilton-Jacobi equations
Semiclassical propagator

Reading:
--------
	Classical and Quantum Chaos	
        ---    www.nbi.dk/ChaosBook/postscript.html

	print (if anything) pp. 461-429
		chapter 21 - Semiclassical evolution 

Problem set:
------------
The object is to get refresh/learn a little bit about Dirac delta fct
formalism and about Hamilton's equations.
        21.A) Verify Green's function Laplace transform (21.12),
	      argue that positive \epsilon is needed
	      (hint: look at a good quantum mechanics textbook)
        21.B) Derive representation (21.15) of a delta function
	      as imaginary part of a 1/x
	      (hint: read up on principal parts, positive and
               negative frequency part of the delta function,
	       perhaps Cauchy theorem in a good QM of field theory,
	       or ... book)
        21.C) Verify the decomposition of Schroedinger equation
	      into real, imaginary parts, eqs. (21.21) and (21.22)

due Tue 22 2002, in the class or Predrag's mailbox.

Evaluation method:
-----------------
Weekly homework assignments and a term project individually tailored
to student's level and research interests.
Grades will be determined from the homework (60%) and the term project (40%).