Express the wavefunction \(\phi(q,t)\) in terms of an integral of the initial state \(\phi(q,0)\)


 * 1) Write the wavefunction \(\phi(q,t)\) in Dirac bracket form: \(\phi(q,t) = \langle q|\phi(0,t)\rangle\)
 * 2) Take out the time dependence as an exponential: \(\phi(q,t) = \langle q|e^{i\hat{\mathcal{H}}t/\hbar}|\phi(0)\rangle\)
 * 3) Insert the identity operator: \(\phi(q,t) = \langle q|e^{i\hat{\mathcal{H}}t/\hbar} \mathbb{I}|\phi(0)\rangle\)
 * 4) Use the completeness of states for Hilbert space \( (\mathbb{I}=\int dq'|q'\rangle\langle q'|) \) to substitute out the identity operator: \(\phi(q,t) = \int dq'\langle q|e^{i\hat{\mathcal{H}}t/\hbar} |q'\rangle\langle q'|\phi(0)\rangle\)
 * 5) Solve the integral: \(\phi(q,t) = \int dq'\langle q|q'(t)\rangle\phi(q')\)