Abstract
We present new symbolic-numeric algorithms for solving the Schrödinger equation describing the scattering problem and resonance states. The boundary-value problems are formulated and discretized using the finite element method with interpolating Hermite polynomials, which provide the required continuity of the derivatives of the approximated solutions. The efficiency of the algorithms and programs implemented in the Maple computer algebra system is demonstrated by analysing the scattering problems and resonance states for the Schrödinger equation with continuous (piecewise continuous) real (complex) potentials like single (double) barrier (well).
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Gusev, A.A. et al. (2015). Symbolic-Numeric Solution of Boundary-Value Problems for the Schrödinger Equation Using the Finite Element Method: Scattering Problem and Resonance States. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_14
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DOI: https://doi.org/10.1007/978-3-319-24021-3_14
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