Hydrogen economy question! i've written my answer below but i'm missing half- equations and the advantages and disadvantages. i'm not even sure whether my answer is right at all. me with this. in advance!

The Schrödinger equation of the hydrogen atom in polar coordinates is:−ℏ22μ[1r2∂∂r(r2∂ψ∂r)+1r2sinθ∂∂θ(sinθ∂ψ∂θ)+1r2sin2θ∂2ψ∂ϕ2]−Ze24πϵ0rψ=EψBoth LHS and RHS contain a term linear in ψ, so combine:1r2∂∂r(r2∂ψ∂r)+1r2sinθ∂∂θ(sinθ∂ψ∂θ)+1r2sin2θ∂2ψ∂ϕ2+2μℏ2(E+Ze24πϵ0r)ψ=0

The density would be 1.622