3 Scattering: a stationary-state approach
Scattering calculations using wave packets are so laborious that they are generally done numerically, using a computer. However, in many cases, scattering phenomena can be adequately treated using a procedure based on stationary states. This approach can give valuable insight into the scattering process without the need for computer simulations.
Session 3 introduces the stationary-state approach to scattering. The discussion is mainly confined to one dimension, so a stationary-state solution to the Schrödinger equation can be written in the form
where (x) satisfies the appropriate time-independent Schrödinger equation at energy E. The first challenge is to find a way of interpreting stationary-state solutions that makes them relevant to an inherently time-dependent phenomenon like scattering.