Let Psi(x,0)=E^(ik0x) when x=(-a/2,a/2) and zero elsewhere. 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.