Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schroedinger equation

Journal Article · Fri Oct 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.042103· OSTI ID:20646333

Szmytkowski, Radoslaw; Bielski, Sebastian ^[1]

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1. Atomic Physics Division, Department of Atomic Physics and Luminescence, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, PL 80-952 Gdansk (Poland)

The embedding method [J. E. Inglesfield, J. Phys. C 14, 3795 (1981)] for computing bound states of the Schroedinger equation is reformulated in terms of the Dirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) surface integral operators. Variational principles for energy, allowing the use of trial functions which are discontinuous in values or derivatives, are employed. A method of constructing kernels of the DtN and NtD operators from solutions to an auxiliary Steklov (Stekloff) eigenproblem is presented. Numerical results illustrating the usefulness of the DtN and NtD embedding methods are provided. After necessary modifications, the DtN-NtD formalism presented in this work may constitute the convenient framework for generalizing the embedding method to bound states of the Dirac equation.

• OSTI ID: 20646333
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOUND STATE
DIRAC EQUATION
INTEGRAL EQUATIONS
KERNELS
MATHEMATICAL SOLUTIONS
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SURFACES
VARIATIONAL METHODS