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Symbolic-numeric solution of boundary-value problems for the Schrödinger equation using the finite element method: scattering problem and resonance states. (English) Zbl 1434.65101

Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 17th international workshop, CASC 2015, Aachen, Germany, September 14–18, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9301, 182-197 (2015).
Summary: 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).
For the entire collection see [Zbl 1321.68010].

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
68W30 Symbolic computation and algebraic computation

Software:

KANTBP; Maple
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