Kantorovich Method for Solving the Multi-dimensional Eigenvalue and Scattering Problems of Schrödinger Equation

  • Ochbadrakh Chuluunbaatar
  • Michael S. Kaschiev
  • Vera A. Kaschieva
  • Sergey I. Vinitsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)


A Kantorovich method for solving the multi-dimensional eigenvalue and scattering problems of Schrödinger equation is developed in the framework of a conventional finite element representation of smooth solutions over a hyperspherical coordinate space. Convergence and efficiency of the proposed schemes are demonstrated on an exactly solvable model of three identical particles on a line with pair attractive zero-range potentials below three-body threshold. It is shown that the Galerkin method has a rather low rate of convergence to exact result of the eigenvalue problem under consideration.


Eigenvalue Problem Galerkin Method Helium Atom Identical Particle Hyperspherical Harmonic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ochbadrakh Chuluunbaatar
    • 1
  • Michael S. Kaschiev
    • 2
  • Vera A. Kaschieva
    • 3
  • Sergey I. Vinitsky
    • 1
  1. 1.Joint Institute for Nuclear ResearchMoscow regionRussia
  2. 2.South - West University Neofit RilskiBlagoevgrad, Bulgaria
  3. 3.Department of MathematicsTechnical University - SofiaBulgaria

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