Consider a quantum mechanical system described by the Hamiltonian operator \(\hat H\), with eigenfunctions \(\psi_n\) and corresponding eigenvalues \(E_n\) such that: \(H^{ψ_n}=E_nψ_n\)

where $n = 0, 1, 2, \dots$ , and the eigenvalues are ordered as \(E_0≤E_1≤E_2≤….\)

An arbitrary wavefunction \(\psi\) is expanded in terms of these eigenfunctions as: \(Ψ=n∑c_nψ_n\)

where $_{c n}$ are complex coefficients.

The expectation value of the Hamiltonian \(\hat H\) for this wavefunction $\Psi$ is given by:\(⟨\hat H⟩=\frac{∑_n∣c_n∣^2E_n}{∑_n∣c_n∣^2}\)

Which of the following statements about the expectation value \(<\hat H>\) is correct?