Perturbation theory results:

First-order energies: $E_1^{(1)} = 0$, $E_2^{(1)} = 0$. - Second-order energies: $E_1^{(2)} = |V|^2/(0 - \Delta) = -V^2/\Delta$ and $E_2^{(2)} = |V|^2/(\Delta - 0) = +V^2/\Delta$.