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Download Specialization: 010600/52 Program: Applied Mathematics and Physics Program director: prof. S.L. Yakovlev
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Transcript
Specialization: 010600/52 Program: Applied Mathematics and Physics Program director: prof. S.L. Yakovlev Department of computational physics Scientific advisor: Ph.D Yarevsky E. A. Reviewer: Mgr. Gradusov V. A. Deal.ii as a tool to study bound states and scattering problems in three-body quantum systems Shmeleva Yulia Few-body quantum mechanical problem is well-known challenging problem in quantum mechanics. Several successful approximation techniques have been developed for few-body problem, including the Hartree Fock method, finite difference methods and finite element method (FEM). One of the available implementations of the FEM is Deal.ii library. Deal.ii is a powerful general purpose object oriented finite element differential equations analysis library, that provides a wide collection of tool classes such as adaptive meshes, a variety of finite elements, parallelization and many other routines. Use of such a frameworks will significantly simplify the process of writing the program code and let the researcher concentrate on the physical or technical problem itself. The aim of the present work is to explore deal.II and to evaluate its efficiency, stability and accuracy for quantum mechanical problems. The helium atom with zero total angular momentum has been chosen as a benchmark of the three-body Coulomb problem. Both the exact threedimensional Schrodinger equation and the two-dimensional S-wave model have been investigated. The ground state energy has been calculated and compared to the high precision results. Convergence properties and the accuracy of the energy spectrum have been analyzed on static and adaptive grids. The results show that Deal.ii library can be successfully used for accurate quantum mechanical calculations while it is not always efficient. The list of the publications 1. Y. Shmeleva “Deal.ii library as a tool to study three-body quantum systems”, Book of abstracts of the International Student Conference “Science and Progress 2011”. — 2011. — p. 212 Scientific adviser Ph.D. Yarevsky E. A. Reviewer Mgr. Gradusov V. A.
