The Stark effect is the splitting of Hydrogen atom spectral lines if that atom is in homogeneous
electric field. This Quantum Mechanics problem is about Stark effect that will be calculated with
degenerated time-independent perturbation theory.
Hydrogen atom with $H_0$ Hamiltonian and $L_z$ angular momentum component has eigen vector
of $|n, l, m >$.
The first four excitation state (n = 2) of Hydrogen atom in $|n, l, m >$ term is degenerated
because they have same energy $E_2^{(0)} = -\frac{e^2}{8a_0}$. Calculate that energy in eV!
A handy note:
$\psi_{2,0,0}(\vec{r}) = \frac{1}{\sqrt{32\pi a_0^3}} \left(2 - \frac{r}{a_0}\right) e^{-\frac{r}{2a_0}}$
$\psi_{2,1,0}(\vec{r}) = \frac{1}{\sqrt{32\pi a_0^3}} \frac{r}{a_0} \cos\theta e^{-\frac{r}{2a_0}}$
