NONLINEAR DYNAMICS: QUANTUM CHAOS ----------------------------------------------------------- Georgia Tech PHYS 7224 Spring semester 2004 Predrag Cvitanovic' Lecture 3: Thu Jan 15 2004 09:35-10:55 in Howey S104 WKB quantization ---------------- 1-d quantization by means of the WKB ansatz and Maslov's trick. Main message: leakage of a wave function into forbiden regions induces a phase loss of \pi/2 for each classical turning point. Reading: -------- Chaos: Classical and Quantum (version 10) --- ChaosBook.org/stable/postscript.html print (if anything) pp. 419-426 chapter 24 - WKB quantization Problem set I ------------- (numbers refer to version 10 of ChaosBook) I-1 Verify Green's function Laplace transform (23.15), argue that positive \epsilon is needed (hint: look at a good quantum mechanics textbook) I-2 Derive representation (23.18) of the Dirac delta(x) 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 textbook) Exer 24.6 Derive the Fresnel integral (24.13). due Thu, Jan 22 2004, in the class or Predrag's mailbox. Evaluation method: ----------------- 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%).