Time Evolution of Stationary States

A particle in quantum mechanics has the non-normalized wavefunction at \(t=0\):

\[\psi(x) = -i \phi_1 + \phi_3,\]

where the \(\phi_n\) are the orthonormal eigenstates of some Hamiltonian with energies \(E_n = \frac{1}{n}\).

Find the normalized wavefunction \(\psi(x,t)\) at all times.

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