I could not understand this solution. is there any other way this can be done?

Example: Consider a particle of mass m and charge g place in uniform field E = E,i. Apart from this a restoring force corresponding to the potential V(x) =mo X acts. Find the lowest 2 energy eigen value. Consider the electric field is originated at origin. Solution: The electric potential energy at the position x will be gEx So the effective potential 1s given by 1 Vx)mo X-qEr 1 qE 2m So Hamiltonion