a) Find the momentum space representation of the plane wave state $\psi(t, x) = \frac{1}{\sqrt{2\pi\hbar}}e^{i(p_0x/\hbar - p_0^2t/2m\hbar)}$ b) Find the probability current (see Homework 9) associated to $\psi(t, x)$. Try to simplify your result as much as possible.
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The Fourier transform of a function f(x) is given by: F(p) = ∫ f(x) e^(-ipx/ħ) dx In this case, we have f(x) = Ψ(t,x) = e^(i(p₀x/ħ - pₐt/2mħ))/2πħ. So, we need to find F(p). F(p) = ∫ e^(i(p₀x/ħ - pₐt/2mħ))/2πħ e^(-ipx/ħ) dx Let's simplify this expression by Show more…
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