Schrodinger Equation in Dilated Frame

There has been interest in the form of the Schrodinger equation in different noninertial frames for many decades, especially the rotating frame. Recently, transforming from one frame to another is described by using Lorentz boosts followed by a nonrelativistic limit (1). In this note, we consider the case of dilating objects which expand in such a way that the change in density is constant throughout the body. We then try to obtain a time-independent Schrodinger equation in the dilating frame. The results seem to be similar to the rotating case, although there the generator is  Lz= rxp while for the dilating case, it is r dot p. It is possible that such a scenario of dilation may apply to heavy nuclei which have undergone a collision, are heated and are expanding slowly.