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For solving the time dependent Schrödinger equation ##H|\psi(t) \rangle = i\hbar \frac{\partial}{\partial t}|\psi (t)\rangle##, I read in quantum mechanics books the assumption about the solution ##|\psi(t) \rangle## which is made of a linear combination of a complete set of the stationnary states ##|\phi(t) \rangle ## (that form a vectorial space) as: $$|\psi(t) \rangle = \sum_n c_n(t) |\phi_n(t) \rangle $$.

__My question__:

When it is not easy to find stationnary states of the Schrödinger equation, is it correct to use a linear combination of another complete set of function say ##|f(t) \rangle ## (that form a vectorial space) to construct the solution ##|\psi(t) \rangle##?

Thanks.