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Solution of Quantum Mechanical Problems Using Finite Element Method and Parametric Basis Functions

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Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

New computational schemes, symbolic-numerical algorithms and programs implementing the high-accuracy finite element method (FEM) for the solution of quantum mechanical boundary-value problems (BVPs) are reviewed. The elliptic BVPs in 2D and 3D domains are solved using the multivariable FEM and Kantorovich method using parametric basis functions. We demonstrate and compare the efficiency of the proposed calculation schemes, algorithms, and software by solving the benchmark BVPs that describe the scattering on a barrier and a well, the bound states of a helium atom, and the quadrupole vibration in a collective nuclear model.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, 141980, Russia

    O. Chuluunbaatar, S. I. Vinitsky, A. A. Gusev & P. M. Krassovitskiy

  2. National University of Mongolia, Ulan-Bator, 210646, Mongolia

    O. Chuluunbaatar

  3. RUDN University, Moscow, 117198, Russia

    S. I. Vinitsky

  4. Saratov State University, Saratov, 410012, Russia

    V. L. Derbov

  5. Institute of Nuclear Physics, Almaty, 050032, Kazakhstan

    P. M. Krassovitskiy

Authors
  1. O. Chuluunbaatar
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  2. S. I. Vinitsky
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  3. A. A. Gusev
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  4. V. L. Derbov
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  5. P. M. Krassovitskiy
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Corresponding author

Correspondence to S. I. Vinitsky.

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Chuluunbaatar, O., Vinitsky, S.I., Gusev, A.A. et al. Solution of Quantum Mechanical Problems Using Finite Element Method and Parametric Basis Functions. Bull. Russ. Acad. Sci. Phys. 82, 654–660 (2018). https://doi.org/10.3103/S1062873818060096

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  • DOI: https://doi.org/10.3103/S1062873818060096

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