NONLINEAR DYNAMICS: QUANTUM CHAOS  
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	Georgia Tech PHYS 7224			Spring semester 2002  
	Predrag Cvitanovic'

	Lecture 21         Thu, Mar 28 2002 12:05-13:25 in Howey S106

Helium, classical dynamics
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In continuing episode of foolish optimism I continue discussing quantization
of helium - symmetries, symbolic dynamics.

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

chapter 24 - Helium atom
	24.1 Classical dynamics
	     Exercises
	
Problem set 
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Exer 24.1 KS transformation.
	Derive the Kustaanheimo--Stiefel version of the collinear
	helium equations of motion.
 
Exer 24.3  Helium trajectories.
	Do some trial integrations of the collinear helium.
	Most trajectories will run away, do not be surprised -
	the classical collinear helium is unbound.
	Try to guess approximately the shortest cycle of fig 24.5.
 
Exer 24.4  A Poincare section for collinear Helium.
	Construct the Poincare section of 24.3b.
	Try to delineate regions which correspond to finite
	symbol sequences.

Perhaps some of the helium stuff on http://www.nbi.dk/ChaosBook/extras
might help you.
 

	DUE: Tue, Apr 2 2002

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The solution of problems starting with these three and ending with
the helium spectrum form the final exam in the course. 

If you prefer, 
you can compute the 3-disk resonances instead, the determination
of perioidc orbits is easier in billards than it is in the flows.
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