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Let $A$ and $B$ be finite-dimensional Hermitian matrices, and let $v$ $:=$ $max${$||A||,||B||$}.

Show that $||(e^{-iAt/m}e^{-iBt/m})^m -e^{-i(A+B)t}||\leq\epsilon$ provided $m = \Omega(v^2t^2/\epsilon)$.

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    Is that supposed to be a 2-norm?2010-11-26
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    It is generally considered impolite to phrase your questions in the imperative voice. If this is homework, you should also indicate what you've done so far and where you've gotten stuck. It is not our job to do your homework for you every time you tell us to.2010-11-26

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