Download Specialization: 010600/52 Program: Applied Mathematics and Physics Program director: prof. S.L. Yakovlev

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.