Quantum scattering in one dimension
  A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion. 
Vania E. Barlette, Marcelo M. Leite and Sadhan K. Adhikari