Electronic wave propagation with Mathematica. A highly accurate and effective scheme for solving the time dependent Schrodinger equation is implemented using Mathematica. The present code named Chebyshev.m achieves a precision of one part in 10 -17 , which is found to be independent of time steps. With a new wavefunction splitting algorithm and a more efficient method for evaluating transmission coefficients, the improved code requires considerably less CPU time than reported in the authors’ previous paper [Phys. Rev. A 57, 3554 (1998)]. Further, implementation in Mathematica allows the code to be used in a cohesive and interactive environment which is nevertheless computationally powerful. The interactive nature of this environment also makes the functions in this package suitable for use in undergraduate laboratories, where “real life” potentials could be easily studied. It is an important and meanigful addition to the electronic wave propogation literature.

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  1. Falloon, P.E.; Wang, J.B.: Electronic wave propagation with Mathematica (2001)