<P> The Hamiltonian of the hydrogen atom is the radial kinetic energy operator and coulomb attraction force between the positive proton and negative electron . Using the time - independent Schrödinger equation, ignoring all spin - coupling interactions and using the reduced mass μ = m e M / (m e + M) (\ displaystyle \ mu = m_ (e) M / (m_ (e) + M)), the equation is written as: </P> <P> (− ħ 2 2 μ ∇ 2 − e 2 4 π ε 0 r) ψ (r, θ, φ) = E ψ (r, θ, φ) (\ displaystyle \ left (- (\ frac (\ hbar ^ (2)) (2 \ mu)) \ nabla ^ (2) - (\ frac (e ^ (2)) (4 \ pi \ epsilon _ (0) r)) \ right) \ psi (r, \ theta, \ phi) = E \ psi (r, \ theta, \ phi)) </P> <P> Expanding the Laplacian in spherical coordinates: </P> <P> − ħ 2 2 μ (1 r 2 ∂ ∂ r (r 2 ∂ ψ ∂ r) + 1 r 2 sin ⁡ θ ∂ ∂ θ (sin ⁡ θ ∂ ψ ∂ θ) + 1 r 2 sin 2 ⁡ θ ∂ 2 ψ ∂ φ 2) − e 2 4 π ε 0 r ψ = E ψ (\ displaystyle - (\ frac (\ hbar ^ (2)) (2 \ mu)) \ left ((\ frac (1) (r ^ (2))) (\ frac (\ partial) (\ partial r)) \ left (r ^ (2) (\ frac (\ partial \ psi) (\ partial r)) \ right) + (\ frac (1) (r ^ (2) \ sin \ theta)) (\ frac (\ partial) (\ partial \ theta)) \ left (\ sin \ theta (\ frac (\ partial \ psi) (\ partial \ theta)) \ right) + (\ frac (1) (r ^ (2) \ sin ^ (2) \ theta)) (\ frac (\ partial ^ (2) \ psi) (\ partial \ phi ^ (2))) \ right) - (\ frac (e ^ (2)) (4 \ pi \ epsilon _ (0) r)) \ psi = E \ psi) </P>

Who formulated the quantum theory for the hydrogen atom