
#1
Apr1211, 03:47 AM

P: 1,863

1. The problem statement, all variables and given/known data
Hi guys In my book they use the following identity [tex] e^{  i\widehat Ht/\hbar } = e^{  i\widehat Tt/\hbar } e^{  i\widehat Vt/\hbar } + O(t^2 ) [/tex] where H = T+V, and the last term means "terms of order t^{2} 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(t^{2}) 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. 



#2
Apr1211, 03:58 AM

Emeritus
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Thanks
PF Gold
P: 11,527

Look up the BakerHausdorff lemma.



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