# 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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