Harmonic Oscillator in an Electric Field

consider a particle with charge e moving under three dimensional isotropic harmonic potential l

$V(r)={\frac {1}{2}}m{\omega }^{2}{r}^{2}$in an electric field $E=E_{0}(x)$ Find the eigen states and eigen values of the patricle

the Hamiltonian of the system is:

${\displaystyle }$