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Can this be a wavefunction of a free particle. I belive it is so because every function of x can be expressed as a wavepacket. Is this correct?

If I want to calculate P(x,0), probability to find the particle between x, x+dx it's just the square of the modulus. But what about P(k,0)? I'm having trouble calculating it's fourier transform, I think that the delta function must show somewhere but I don't know how.

k seems to be certain k=k0 , right? However, P(x,0)=1/a is the same everywhere.