NONLINEAR DYNAMICS: QUANTUM CHAOS
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Georgia Tech PHYS 7224 Spring semester 2002
Predrag Cvitanovic'
Lecture 8 Tue, Feb 5 2002 12:05-13:25 in Howey S106
Gutzwiller trace formula
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Reading:
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Classical and Quantum Chaos
--- www.nbi.dk/ChaosBook/postscript.html
print (if anything) pp. 495-500
chapter 22 - Semiclassical qunatization
Problem set:
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You have been getting off easy because I keep editing and re-editing
the Webbook, without ever getting there... This time, a few exercises
to check how you are surviving the long and difficult derivation of
the Gutzwiller trace formula:
(do not be shy about bugging me about the expostiton in the webbook,
it still needs to be made more reader friendly)
Problem 21.D) Derive the Fresnel integral, eq (21.54) of
chapter 21 - Semiclassical evolution
Problem 21.E) Verify Jacobian manipulations of (21.57)-(21.61) of
chapter 21 - Semiclassical evolution
(warning - there are typos in the text)
Problem 21.F) Verify the coordinate transformation (21.62)-(21.65) of
chapter 21 - Semiclassical evolution
Problem 22.A) Verify Jacobian manipulations leading to the full
phase-space Jacobian (22.2) of
chapter 22 - Semiclassical quantization
and a few exercises to check if the formalism makes sense even in the
simplest cases:
Problem 21.3) 1-dimensional harmonic oscillator in WKB form
chapter 21 - Semiclassical evolution exercises
Problem 21.6) Free particle Hamilton's principal function
chapter 21 - Semiclassical evolution exercises
cases a) and c), case b) optional
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due Tue Feb 12 2002, in the class, or Predrag's mailbox or hand it to Y. Lan.