Atoms that only have one electron are called hydrogenoids. They are hydrogenoids atoms: H, He + , Li 2+ , Be 3+ .
Hydrogen atoms present a factorable wave function in a radial part and a spherical harmonic, which has the form:
$\Psi(r,\theta,\varphi)=R_{n,l}(r)Y_{l,m}(\theta,\varphi)$
where n,l,m are the quantum numbers that make the wave function acceptable.
The energy of a hydrogen atom is given by the expression:
$E_n=\frac{RhZ^2}{n^2}$
As can be seen, the energy depends exclusively on the principal quantum number, n.