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As I understand it, the wavefunction Psi(x) can be written as a sum of all the particle's momentum basis states (which is the Fourier transform of Psi(x)). I was woundering if the wavefunction's complex conjugate Psi*(x) can be written out in terms of momentum basis states, similar to the transform of Psi(x), and if so, what form would it take in order to make make the probability density of Psi(x)Psi*(x) the correct real-valued number.

In other words, if both Psi(x) and Psi*(x) were written out in their Fourier transform forms, and multiplied together in these forms, what would the transform of Psi*(x) look like?

Any insight into this would be greatly appriciated.

-Andrew