# QM: Identity

by Niles
Tags: identity
 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). Best, Niles.
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,527 Look up the Baker-Hausdorff lemma.

 Related Discussions Atomic, Solid State, Comp. Physics 0 Calculus & Beyond Homework 3 Calculus & Beyond Homework 6 Calculus & Beyond Homework 10 Calculus & Beyond Homework 1