Let's assume there is some overlap between the ansatz and the ground state (otherwise, it's a bad ansatz). We wish to normalize the ansatz, so we have the constraints ⟨ ψ ψ ( α α ) | ψ ψ ( α α ) ⟩ = 1 and we wish to minimize ε ε ( α α ) = ⟨ ψ ψ ( α α ) | H | ψ ψ ( α α ) ⟩ .