We are considering the solution to Schrödinger’s equation for scattering of an incoming plane wave in the z -direction by a potential localized in a region near the origin. We are, obviously, interest...We are considering the solution to Schrödinger’s equation for scattering of an incoming plane wave in the z -direction by a potential localized in a region near the origin. We are, obviously, interested only in the outgoing spherical waves that originate by scattering from the potential, so we must be careful not to confuse the pre-existing outgoing wave components of the plane wave with the new outgoing waves generated by the potential.
Firstly we transform the problem to the center of mass reference frame where it becomes that of a single effective particle of mass μ=mM/(m+M) moving in a hard sphere potential \((V (r < r_H...Firstly we transform the problem to the center of mass reference frame where it becomes that of a single effective particle of mass μ=mM/(m+M) moving in a hard sphere potential (V(r<rH=XM+xm)=∞). In fact, though, the analysis is correct and closer analysis of the θ dependence of the wavefunction shows that half the amplitude is diffracted into the classical ‘shadow’ of the sphere to cancel the amplitude of the unscattered wave there.
