I am new to QM, have find some wavefunction in different potentials, but there we need to normalize the wave function, for a reason that - particle should be found somewhere . So a wave-function, to be related to a particle need to be normalizable. But in scattering, there is no notion of normalization!
Aren't the solutions in scattering states related to some particle?
Mathman - when we study scattering we assume that we have a flux of multiple particles headed at some target and the question we want to answer is "which way do they go when they bounce off?". The end result of the endeavor is to find the relative intensity of the deflected flux in any given direction.
Since we imagine the end result for any given scattered particle will look like a plane wave it can't be normalized in the sense of, say, an atomic orbital. To put this another way, atomic orbitals are bound states and can be normalized. Incoming flux and outgoing scattering are plane waves - and the analogy to normalization would be conservation of flux.
