Fall 2009 Homework Assignments
Problems 2.14 and 2.17 in the textbook.
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) .
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 .
Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.