- #1
plmokn2
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Sorry for not following the template but as I'm not answering a problem it didn't seem apropriate. Hopefully this is the right place to put this (it seems somewhere between introductory and advanced).
Just when I thought I was getting my head round this stuff I'm completely stuck on how the two lines in the section of the book I'm reading follow from the first line. Any explanation would be appreciated please.
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
Just when I thought I was getting my head round this stuff I'm completely stuck on how the two lines in the section of the book I'm reading follow from the first line. Any explanation would be appreciated please.
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