1. The problem statement, all variables and given/known data Consider the full 1-electron hydrogen wave function. Prove that ψ =A(6r –r2/a0) exp[-^r3/a0] sinθ exp[+iφ], is a solution to the Schrodinger equation H|ψ> = E|ψ>, where H is the Hamiltonian operator. Hence show that it's energy E= -1.51 eV and its principle quantum number n = 3. 2. Relevant equations So as far as I understand the Schrodinger equation is -ħ2/2m[1/r2 δ/δr(r2 δ/δr) + 1/(r2sinθ) ∂/∂θ(sinθδ/δθ) + 1/(r2sinθ) δ2/δφ2]ψ - Vψ = Eψ 3. The attempt at a solution I have subbed the solution into the equation, differentiating where needed and so on. I'm unsure as to what actually proves it is a solution, do I need to get one side equal to zero? I also have no idea how to show that its E = -1.51 eV. I would be able to get from E to n though.