Sorry for all the dull questions, but I just when I thought I was getting my head round this stuff I'm completly stuck on how the two lines in the section of the book I'm reading follow from the first line.
For context it's derived the propagator for a particle in free space (H=P^2/2m) (all in 1 dimension) so:
|E> = a|p=(2mE)^1/2> + b|p=-(2mE)^1/2>
for arbitary a,b.
Giving a propagator:
U(t)=INT( |p><p|exp(-iEt/hbar) from minus infinity to plus infinity where E is the energy eigenvalue=p^2/2m since it's degenerate.
The book is then evaluating the propagator (U) explicitly in the X basis.
I've done the rest in math type to hopefully make it readable:
http://i196.photobucket.com/albums/aa266/plmokn_02/prop.jpg
Thanks very much (and sorry for being a pain)