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
