Symbolic-numeric solution of boundary-value problems for the schrodinger equation using the finite element method: Scattering problem and resonance states

Abstract

We present new symbolic-numeric algorithms for solving the Schrodinger 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 Schrodinger equation with continuous (piecewise continuous) real (complex) potentials like single (double) barrier (well).