NONLINEAR DYNAMICS: QUANTUM CHAOS
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Georgia Tech PHYS 7224 Spring semester 2002
Predrag Cvitanovic'
Lecture 3: 12:05-13:25 Thu Jan 15 2002 in Howey S106
Semiclassical propagation
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Hamilton-Jacobi equations
Semiclassical propagator
Reading:
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Classical and Quantum Chaos
--- www.nbi.dk/ChaosBook/postscript.html
print (if anything) pp. 461-429
chapter 21 - Semiclassical evolution
Problem set:
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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:
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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%).