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In Griffiths QM, it is claimed that to solve the Schrodinger Equation, we take the solution wavefunction [itex]\Psi(x,t)[/itex] to be of a seperable form [itex]\psi(x)\phi(t)[/itex].

He then says that a superposition of these seperable forms can always give us the general solution. Can someone help me prove that statement? How do I know that every solution [itex]\Psi(x,t)[/itex] is a linear combination of solutions of the form [itex]\psi(x)\phi(t)[/itex]

Thank you!

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# Schrodinger Equation and seperation of variables

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