Discussion
In scattering theory of spherically symmetric potential, the incident particles on z-axis are represented by :
Answer: A
The incident particles are represented by \(A\exp(ikz)\).
In scattering theory the wave function far from the target is written as an incoming plane wave plus an outgoing spherical wave:
\[ \begin{aligned} \psi &\approx Ae^{ikz} \\ &\quad + Af(\theta)\frac{e^{ikr}}{r} \end{aligned} \]
The plane wave \(Ae^{ikz}\) describes the beam of incident particles travelling along the z-axis with momentum \(\hbar k\), with uniform probability density.
A factor 1/r belongs to the spherical scattered wave, whose amplitude falls with distance so that probability flux is conserved through larger spheres; \(1/r^{2}\) and a factor r have no place in the incident beam.
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