Collision of a Free Particle with a Potential Field

Abstract

In the previous chapter we discussed the motion of a free particle. Now we consider the collision (scattering) of a free particle with (by) a potential field. In the presence of a potential, Eq. (2.3.3) changes to (Burke, 1977)

$$ \left[ { - \begin{array}{*{20}{c}} {{\hbar ^2}}\\ {\overline {2m} } \end{array}{\nabla ^2} + V(r)} \right]\Psi (r) = E\Psi (r) $$

(1)

where V _(r) is the potential energy of the particle. In the asymptotic region, where V _(r) = 0, (3.1.1) admits two solutions.