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ehrenfest
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Homework Statement
Exercise 5.1.1 : Show that Eq (5.1.9( may be rewritten as an integral over E and a sum over the +/- index as
[tex]U(t) = \sum_{a=\pm}\int^{\infty}_{0}|E,a><E,a|e^{-iEt/\hbar}dE[/tex]
You will find at http://books.google.com/books?id=2z...sig=dZ4WX7ruNL46QZzNSbqIExbz3qw#PRA1-PA152,M1 equation 5.1.9 and the background of this problem.
Homework Equations
The Attempt at a Solution
I am trying to use the substitution rule starting with 5.1.9 which requires that we tack on a 2m/sqrt(2mE) to get and integrand that looks like
[tex]\frac{2m}{(2mE)^{1/2}}|p><p|e^{-iEt/\hbar}dE[/tex]
I am not sure how you deal with the limits of integration, how we get rid of the 2, and how you deal with the eigenvectors. Do we need to change anything for the eigenvectors since they are the same for both p and E?
Please just give me hints not the entire solution. Thanks.
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