Electronic wave propagation with Mathematica (Q5932760)

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)].NEWLINENEWLINENEWLINEFurther, 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.