Square root of differential operator If $D_x$ is the differential operator. eg. $D_x x^3=3 x^2$.
How can I find out what the operator $Q_x=(1+(k D_x)^2)^{(-1/2)}$ does to a (differentiable) function $f(x)$? ($k$ is a real number)
For instance what is $Q_x x^3$?  

Dirac won a Nobel Prize for finding the square root of a pesky differential operator while working on the relativistic Schrodinger equation. http://www.youtube.com/watch?v=zM-Lc16nyho. <--- That video  gives a clear overview of the hacks Dirac used. 
