Final Form

Putting these pieces together, the full function that describes the most basic hydrogen quantum model is given as,

$$\psi_{nlm}=\sqrt{\left(\frac{2}{na}\right)^3\frac{(n-l-1)!}{2n((n... ...ac{2r}{na}\right)^lL^{2l+1}_{n-l-1}\left(\frac{2r}{na}\right)Y^m_l(\theta,\phi)$$ (5.1)

We present this equation in full below.