NONLINEAR DYNAMICS: QUANTUM CHAOS ----------------------------------------------------------- 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 ------------------------- Reading: -------- Classical and Quantum Chaos --- www.nbi.dk/ChaosBook/postscript.html print (if anything) pp. 495-500 chapter 22 - Semiclassical qunatization Problem set: ------------ 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 -------------------------------------------------------------- due Tue Feb 12 2002, in the class, or Predrag's mailbox or hand it to Y. Lan.