# 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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