6.1) Given that $\phi_j$ are orthonormal eigenfunction solutions to the time-independent Schrodinger
equation, $\hat{H}\phi_j = E_j\phi_j$, is the superposition state,
$\Psi(x,t) = \sum_j c_j \phi_j e^{-i\frac{E_j}{\hbar}t}$
a solution to the time-dependent Schrodinger equation? Show your work to justify your
answer. [n.b., Both $\hat{H}$ and the $\phi_j$ are functions of x alone.]