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**1. Homework Statement**

*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. Homework 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.

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