Re: P and H on a segment

mandro writes:
>Now, how, explicitly can one calculate
>that the behavior of the unitary maps
>are those advertised by Dr Baez in his
>previous post. I.e., How can I prove
>explicitly that the unitary map generated
>by P(z) does what he said it does? Ie
>how can I compute exp(iP(z)t) explicitly?

One standard way to do this is to solve for
the eigenfunctions f(z,n,.) and corresponding
eigenvalues lamda(z,n) of P(z), and then use
this formula:

exp(itP(z))[psi](x) =
 sum (exp(it lamda(z,n))) * integral f(n,x) f*(n,x') psi(x') dx'

where the sum is over n.  This assumes that the spectrum is
discrete and relies on the eigenfunctions being a complete
orthornormal set.

nobody