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  1. a)  Write down the one-dimensional time-dependent Schro ̈dinger equation for a wavefunction

    Ψ(t, x) in a potential V (x).

  2. b)  Write down the one-dimensional time-independent Schro ̈dinger equation for a wavefunc-

    tion ψ(x) in a potential V (x).

  3. c)  Assuming that Ψ(t,x) corresponds to an energy eigenstate, write down a mathematical expression that relates the solutions of the one-dimensional time-dependent and time- independentSchro ̈dingerequations,Ψ(t,x)andψ(x).

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