Scattering States

The scattering states are those not bound, where the energy spectrum is a continuous band. Unlike the bound case, the wave-function does not have to vanish at infinity, though a particle can not reflect from infinity often giving a useful boundary condition. At any changes in the potentials, the wave-function must still be continuous and differentiable as for the bound states.

We have to know wave functions and discrete energy levels $E_{n}\!$ for bound state problems; but, for scattering states (unbound states) the energy E isn't discrete. We are interested in obtaining related wave functions in order to use and determine the transmission and reflection coefficients T and R respectively.