The wave function of a particle is given by φ = (1/√5)ψ₁ + (i/2)ψ₂, where ψ₁ and ψ₂ are the normalized eigenfunctions with energies E₁ and E₂ corresponding to the ground state and the first excited state, respectively. The average energy of the Hamiltonian in the state φ is given as:
(a) E₁/5 - E₂/2
(b) (E₀ + 2E₁)/3
(c) (4E₁ + 5E₂)/9
(d) 2E₁ - (5/2)E₂