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

	Georgia Tech PHYS 7224			Spring semester 2004  
	Predrag Cvitanovic'

        Lecture 3:        Thu Jan 15 2004
	                  09:35-10:55 in Howey S104

WKB quantization
----------------
1-d quantization by means of the WKB ansatz and Maslov's trick.
Main message: leakage of a wave function into forbiden
regions induces a phase loss of \pi/2 for each classical
turning point.


Reading:
--------
	Chaos: Classical and Quantum   (version 10)
        ---    ChaosBook.org/stable/postscript.html

	print (if anything) pp. 419-426
		chapter 24  - WKB quantization

Problem set I 
-------------
(numbers refer to version 10 of ChaosBook)

        I-1   Verify Green's function Laplace transform (23.15),
	      argue that positive \epsilon is needed
	      (hint: look at a good quantum mechanics textbook)

        I-2   Derive representation (23.18) of the Dirac delta(x)
	      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 textbook)

Exer   24.6   Derive the Fresnel integral (24.13).


due Thu, Jan 22 2004, 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%).