Abstract
The following is a summary of a series of tutorial lectures given at the Institute for Mathematics and its Applications during a Workshop on Waves and Scattering during the Spring, 1995. The purpose was to provide a little background in computational methods that have been developed over the past several decades by quantum dynam- icists. Most of these techniques have been developed without worrying about mathematical details, with the primary objective being to apply them to specific systems. It is not possible to give an exhaustive account of all the methods that have been used, but hopefully a sufficiently wide range is given to enable one to obtain a general sense of the types of methods that have been brought to bear. Both time-independent and time- dependent approaches are discussed, and representative references to the literature given to facilitate the interested reader to obtain more details. For the most part, we have restricted ourselves to simple one-dimensional (1D) problems in order to illustrate the strategies, but the methods are more general and have been applied to real problems of varied complexity. In general, the systems of interest are conservative ones, although at least one computational method is discussed which can be applied to systems with an explicitly time dependent Hamiltonian. Finally, in addition to discussing computational techniques, we also give a brief outline of how one extracts the physically meaningful or measureable quantities from solutions of the Schrödinger equation (since this also may not be familiar to the non-specialist in quantum scattering).
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References
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).
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Kouri, D.J., Hoffman, D.K. (1997). A Tutorial on Computational Approaches to Quantum Scattering. In: Truhlar, D.G., Simon, B. (eds) Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics. The IMA Volumes in Mathematics and its Applications, vol 89. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1870-8_2
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