A definite-momentum wavefunction can be expressed by the formula Ψ(x)=A(coskx+isinkx), where A and k are constants.
((a)) How is the constant k related to the particle's momentum? (Justify your answer.)
((b)) Show that, if a particle has such a wavefunction, you are equally likely to find it at any position x.
((c)) Explain why the constant A must be infinitesimal, if this formula is to be valid for all x.
((d)) Show that this wavefunction satisfies the differential equation dΨ/dx=−ikΨ.
((e)) Often the function cosθ+isinθ is written instead as eiθ. Treating the i as an ordinary constant, show that the function Aeikx obeys the same differential equation as in part (d).