Expectation of the Hamiltonian

A particle of mass \(m\) is trapped in an infinite square well of width \(L\). The particle is characterized by the wavefunction \[\Psi(x,t) = \frac{4}{5}{\psi}_{1}{e}^{-{E}_{1} t / \hbar}-\frac{3}{5}{\psi}_{3}{e}^{-{E}_{3} t / \hbar}\]

The expectation value of the Hamiltonian operator is given by

\[\left<\hat{H} \right>= \frac{A{\hbar}^{2}{\pi}^{2}}{Bm{L}^{2}}.\] Find \(A \div B\).

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