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{\bf  COMPUTATIONAL PROBLEMS IN THE\\
ADIABATIC REPRESETATION METHOD }  \\
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{\bf
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 M.S.Kaschiev  \\
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 Institute of Mathematics, Acad.G.Bontchev Str., Bl.8, Sofia 1113, Bulgaria \\
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A numerical method for solving the 3D Schroedinger bound states problem is
considered.  This method is known as an adiabatic representation method. We use
hyperspherical coordinates. The method considered successfully reduces given 3D
problem to an eigenvalue problem for a system of second order ODE. The main
problems we solved are:

1. A choise of two -- dimentional hyprespherical basis;

2. The calculation of effective potentials;

3. To find the eigenvalues and eigenfunctions of system of hyperradial
equations.

A discretization of all problems is based on the FEM. For 2D problem we use 8
-- node isoparametric FEM, for the 3--th one --- Lagrange elements of order 1,
\ 2, ...., 10.

The accuracy is demonstrated using the test, having an analytical solution. As
an example we consider the three body quantum mechanics problem -- the system
$Ps^-$.
The numerical results show a very fast convergence and high accuracy of the
method.


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