Close. In three dimensions the time-independent Schrodinger equation for the wavefunction (in Cartesian coordinates) is
-\frac{\hbar^2}{2m}\nabla^2\psi (x,y,z) + U(x,y,z)\psi(x,y,z) = E\psi(x,y,z)
where \nabla^2 is the Laplacian. You could also express this in coordinate systems other than...