a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a wavefunctionΨ(t, x) in a potential V (x).b) Write down the one-dimensional time-independent Schro ̈dinger equation for a wavefunc-tion ψ(x) in a potential V (x).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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Question

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

Ψ(t, x) in a potential V (x).
b) Write down the one-dimensional time-independent Schro ̈dinger equation for a wavefunc-

tion ψ(x) in a potential V (x).
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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