Dispersion in Chromatography Columns - Dispersion Processes that take Place in an LC Column > Longitudinal Diffusion > The Diffusion Process > Page 16

or                           

                    Now  as  ,

  then 

 

         or,                                                         (6)

Now, this is a standard differential equation and one solution to this equation, which can be proved by appropriate differentiation,  takes the Gaussian form as follows: