Well just apply the Hamiltonian onto the state psi. this state is the sum of three phiterms. So each phistate yields :
[tex]H \phi_1 = E_1 \phi_1[/tex]
[tex]2H \phi_2 = 2E_2 \phi_2[/tex]
[tex]3H \phi_3 = 3E_3 \phi_3[/tex]
Just add up everything and you get :
[tex]H \Psi =\frac {1}{\sqrt14} (E_1 \phi_1 + 2E_2 \phi_2 + 3E_3 \phi_3)[/tex]
The clue is to write down each energy term as a function of [tex]E_1[/tex]. You have a formula given to do that. Keep in mind that the coefficients of the psiwavefunction denote the possible energy values for the system
Good Luck
marlon
