SOLVING TIME-DEPENDENT EQUATIONS OF SCHRÖDINGER-TYPE USING MAPPED INFINITE ELEMENTS

Jairo Duque ()
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Jairo Duque: Departamento de Matemáticas, Universidad del Valle, Calle 13 #100-00, Cali, Colombia

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 02, 309-316

Abstract: We present a general technique to solve one-dimensional time-dependent Schrödinger-type equations. A mapped infinite elements approach is used to eliminate spurious reflections of outgoing wave packets from the boundaries of the interval of interest. This procedure leads to more precise solutions because the space coordinates are discretized to approximate the solution in the entire physical domain. We show its utility giving numerical results on three typical examples: a bounded short-range potential; the unbounded potential of a particle in a dc field; and a Hamiltonian with an intrinsic time dependence like the Hamiltonian of a charged particle in an ac electromagnetic field.

Keywords: Finite elements; infinite elements; Crank–Nicolson method; Schrödinger-type equations (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S012918310500711X

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