1. Extensive references and many recent papers describing computational methods for the TDSE can be found in Time-Dependent Quantum Molecular Dynamics, eds. J. Broeckhove and L. Lathouwers, NATO ASI Series B: Physics, Vol. 299 (Plenum, New York, 1992) and in the thematic volume of Computer Physics Communications, Ed. K. Kulander, Vol. 63 (North-Holland, Amsterdam, 1991).
2. See, e.g., any text on quantum scattering theory: R.G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982).
3. See, e.g., J.L. Powell and B. Crasemann, Quantum Mechanics (Addison-Wesley, Reading, MA, 1961) pp. 96–98.
4. This analysis follows the discussion in D.J. Kouri and D.K. Hoffman, Few-Body Systems 18, 203 (1995) and W. Zhu, Y. Huang, D.J. Kouri, M. Arnold, and D.K. Hoffman, Phys. Rev. Lett. 72, 1310 (1994) and 73, 1733 (1994); see also D.K. Hoffman, Y. Huang, W. Zhu, and D.J. Kouri, J. Chem. Phys. 101, 1242 (1994).
5. The amplitude density for non-reactive scattering was introduced by B.R. Johnson and D. Secrest, J. Math Phys. 7, 2187 (1966) and generalized to reactive scattering by D.J. Kouri, J. Chem. Phys. 51, 5204 (1969).