QM: Identity

  1. 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).

  2. jcsd
  3. vela

    vela 12,963
    Staff Emeritus
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    Look up the Baker-Hausdorff lemma.
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