Question about the Klein Gordan equation.

cragar

Can i use E=|p|c and use this as my Hamiltonian for the Schroedinger wave equation.
and for p I will use the usual momentum operator. I know people have already tried this stuff.
Is it possible to factor in time-dilation to the Klein Gordan equation. As the wave function evolves in time, does it evolve differently in different frames of reference?
any help would be much appreciated.