Niles
Apr12-11, 03:47 AM
1. The problem statement, all variables and given/known data
Hi guys
In my book they use the following identity
e^{ - i\widehat Ht/\hbar } = e^{ - i\widehat Tt/\hbar } e^{ - i\widehat Vt/\hbar } + O(t^2 )
where H = T+V, and the last term means "terms of order t2 or higher". I can't quite see how they reach this identity. First, I know that T and V do not commute, so I guess that is where the O(t2) comes from.
Any help will be appreciated. (BTW, this is not an exercise problem -- just something in my book that I cannot understand).
Best,
Niles.
Hi guys
In my book they use the following identity
e^{ - i\widehat Ht/\hbar } = e^{ - i\widehat Tt/\hbar } e^{ - i\widehat Vt/\hbar } + O(t^2 )
where H = T+V, and the last term means "terms of order t2 or higher". I can't quite see how they reach this identity. First, I know that T and V do not commute, so I guess that is where the O(t2) comes from.
Any help will be appreciated. (BTW, this is not an exercise problem -- just something in my book that I cannot understand).
Best,
Niles.