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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