Within the square brackets of (11), we convolve the density of scattering matter of atom k with the probability density function for some nuclear displacement. Then, in the curly brackets, we Fourier transform the resulting convolution. The final step is to multiply by a phase depending on the reference (e.g. mean) position of atom k . But, according to the convolution theorem, Fourier transforming a convolution is the same as multiplying the two Fourier transformed functions. Set the displacement between the location in space for which we would like to know the scattering density and the position for the nucleus equal to a new variable v → → = x → → − − x → → k = t → → − − u → → .