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

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 Kanto...

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Bibliographic Details
Published in:Bulletin of the Russian Academy of Sciences. Physics Vol. 82; no. 6; pp. 654 - 660
Main Authors: Chuluunbaatar, O., Vinitsky, S. I., Gusev, A. A., Derbov, V. L., Krassovitskiy, P. M.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.06.2018
Springer Nature B.V
Subjects:
Algorithms
Basis functions
Boundary value problems
Computing time
Finite element analysis
Finite element method
Hadrons
Heavy Ions
Helium
Kantorovich method
Mathematical analysis
Mathematical models
Nonlinear programming
Nuclear models
Nuclear Physics
Physics
Physics and Astronomy
Quadrupoles
Quantum mechanics
ISSN:1062-8738, 1934-9432
Online Access:Get full text
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Summary: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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ISSN:1062-8738
1934-9432
DOI:10.3103/S1062873818060096