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QM: Identity

by Niles
Tags: identity
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Apr12-11, 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

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).

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Apr12-11, 03:58 AM
Sci Advisor
HW Helper
PF Gold
P: 11,673
Look up the Baker-Hausdorff lemma.

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