Developed Theory for The Hydrogen Atom

                      Theory of the Hydrogen Atom
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    For any hydrogenic ion with nuclear charge Z
        V(𝐫) = -Ze²/r

    V(𝐫) = -e²/r

    Eigenfunctions in spherical coordinates:

        Ψₑₗₘ(r,θ,φ) = Rₑₗ(r) Yₗₘ(θ,φ) = Uₑₗ/r Yₗₘ(θ,φ)

    Derived from first principles the wave equation of an electron
    in the hydrogen atom.

        - Start with Dirac Notation

        - transform to eigenvalue equation in position space
            Replace with known special quantities

        - replace pieces with function F and find derivatives
            F = ∑ Cₖρᵏ

        pic 3 first take had factors that needed to be fixed

        - Led to the Laguerre Polynomials
            These are infinite, though, so
            
        - Force Laguerre Polynomial solutions to truncate