• Homework 1: (due Sep. 17, 2009) Problems 1.4 and 1.7 in the textbook.

• Homework 2: (due Oct. 27, 2009)

   Problems 2.14 and 2.17 in the textbook.
  
  

• Homework 2A - required for students who were not in class on Tuesday, Oct. 20; extra credit for others: (due Oct. 22, 2009)

  In the following, |n> , a , and a+ correspond to quantities relevant to the harmonic oscillator problem.
  
  (a) Consider the coherent state |λ> = exp(-λ2/2) exp(λa+) |0> .
  
      Calculate the following quantities:
  
      *   <λ|X|λ>
  
      *   <λ|X2|λ>
  
      *   <λ|P|λ>
  
      *   <λ|P2|λ>
  
      *   (ΔX)(ΔP)
  
  (b) Find the expectation values of the operators X and P for the following states:
  
      * |α> = exp(iqP) |0>
  
      * |α> = exp(ikX) |0>
  
      where q and k are constants. 
  
      Hint: For two operators A and B, and their commutator C = [A,B], if one has [A,C]=0 and [B,C]=0
  
      one then has exp(A+B) = exp(A) exp(B) exp(-C/2) . 
  
  

• Homework 3: (due Nov. 10, 2009)

  
  Using the WKB method, estimate the energy levels for a one-dimensional asymmetric 
  harmonic oscillator with the potential
  
                   { k1x2/2  for  x < 0
            V(x) = {
                   { k2x2/2  for  x > 0 .
  
  Check your result for the case k1 = k2 .
  
  

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