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Time Evolution of Stationary States

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

ψ(x)=iϕ1+ϕ3,\psi(x) = -i \phi_1 + \phi_3,

where the ϕn\phi_n are the orthonormal eigenstates of some Hamiltonian with energies En=1nE_n = \frac{1}{n}.

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


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