The Baker-Hausdorff Formula and a Problem in Crystal Physics

A derivation is given of the Baker-Hausdorff formula for z = ln exey where x and y are noncommuting operators. This result is then used to obtain an expression for z in the case that X = P2 + Q2 and y = αP + βQ, where P and Q are two operators whose commutator P,Q = c is a c number. With the aid of this result a very simple derivation of the expression for the intensity of x rays scattered by the thermal vibrations of a crystal is presented.