Trying out the Schrödinger

Time-independent Schrödinger equation constitutes the following linear eigenvalue problem: find $u : \mathbb{R}^3 \rightarrow \mathbb{C}$ and $\lambda \in \mathbb{C}$ such that
$$-\frac{h^2}{4\pi \mu} \Delta u + V(\boldsymbol{x}) u = \lambda u,$$ where $h$ and $\mu$ are some constants and $V(\boldsymbol{x})$ is a given potential. For hydrogen atom we have
$$V(r) = -\frac{e^2}{4\pi \epsilon_0 r},$$ where $e$ and $\epsilon_0$ are some additional constants and $r$ is the distance from the nucleus. Writing all the constants as one constant
$$C = - \frac{\mu e^2}{\epsilon_0 h^2}$$ and rescaling the eigenvalue leads to
$$-\Delta u - C r^{-1} u = \widetilde{\lambda} u.$$ Let $\Omega$ be the unit ball $B(0,1)$ and consider the homogeneous Dirichlet boundary condition $u|_{\partial \Omega} = 0$. Weak formulation for this problem is: find $u \in H^1_0(\Omega)$ such that
$$(\nabla u, \nabla v)-C(r^{-1}u,v)=\widetilde{\lambda} (u,v)$$ holds for every $v \in H^1_0(\Omega)$.

Setting $C=1$ and solving this with piecewise linear elements on my Matlab FEM code gives eigenvectors whose midsections look as follows:

First 12 lowest eigenvectors of the Schrödinger equation with constants normalized to 1.

You may compare them to the solutions given at Wikipedia. Can you find them all?