Eigen functions of the linear operator L

[nughret]

Hi,
I am looking for eigen functions of the linear operator L defined by

$$L=(-2i(\nablaf).\nabla -i\nabla^2f +(\nablaf)^2)$$

and here f is an abitary function of x,y,z

 

[nughret]

Sorry first (failed) attempt at latex.
L = -2i(grad(f)).grad -i(grad^2(f)) + (grad(f))^2

grad^2 is the laplacian of f