Problem Set One ps or pdf , due Oct 3, 2000
Problem Set Two ps or pdf , due Oct 10, 2000
Problem Set Three ps or pdf , due Oct 17, 2000
Problem Set Four ps or pdf , due Oct 24,2000
Problem Set Five ps or pdf , due Oct 31, 2000
Problem Set Six ps or pdf , due
Problem Set Seven ps or pdf , due Nov 28, 2000
Final Exam: Dec 5 10:30-12:30 in class
NOTE: Problem Set One for Ph 342 ps or pdf
Check here for special Announcments during the quarter. For example, if you find a problem to be ill-defined or unsolvable, check here to see if I have made any corrections to the problem set.
Problem Set 1, in part b) it should have the direct product of V2 with V1, not V1 with V1. Also, it should say the tensor product space is SPANNED by elements of the given form. Finally, do not try to define the sum in the tensor product in terms of the sums defined in V1,V2. Just define the sum as formal linear combinations with scalar coefficients. Thus this problem is more in the nature of "give a definition that makes the tensor product a vector space" than showing that with some given definition the axioms are satisifed.
Problem Set 2, problem 1, please note that the Legendre polynomials are not normalized to have inner product one, but rather 2/(2n+1) for the nth Legendre polynomial.
Problem Set 3, you might find the following formula useful in this problem set:
exp(A) B exp(-A) = B + [A,B] + [A,[A,B]]+ ...
exp(A+B)=exp(A) exp(B) exp(-[A,B]/2)
where in the last formula we must require [A,[A,B]]=[B,[A,B]]=0. These BCH formulae will be proved in class. Note that a consequence of the second formula is
exp(A) exp(B) = exp(B) exp(A) exp([A,B])
Problem Set 7, problem 1(b)(ii) I should have suggested an ansatz which is more general than this with the upper entry of the form $a_1 e^{i \omega_1 t} + a_2e^{i \omega_2 t}$ and a similar linear combination for the lower component.
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