Programs in Physics & Physical Chemistry
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|Manuscript Title: Three-body systems with Coulomb interaction. Bound and quasi-bound S-states.|
|Authors: Evgeny Z. Liverts, Nir Barnea|
|Program title: ThreeBSCbSSR|
|Catalogue identifier: AEPU_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 184(2013)2596|
|Programming language: Mathematica 7-9.|
|Computer: Any PC.|
|Operating system: Any which supports Mathematica; tested under Microsoft Windows 7 and Linux.|
|RAM: < 5GB bytes|
|Keywords: Three-body system, Binding energy, Quasi-bound states, Resonances, Eigenvalues, Eigenvectors, Matrix.|
|Classification: 2.1, 2.8, 2.9, 16.1, 16.10, 17.16.|
Nature of problem:
The Schrödinger equation for three-body system has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations.
The S-wave function is expanded into a triple set of basis functions which are composed of the exponentials combined with the Laguerre polynomials in the perimetric coordinates. Using specific properties of the Laguerre polynomials, solution of the three-particles Schrödinger equation for S-states reduces to solving the generalized eigenvalues and eigenvector problem for the proper Hamiltonian.
Complex scaling method is used for calculating the quasi-bound states.
The basis size is the limiting factor of the method. In practice, up to 104 basis states can be used without any problems.
< 35 minutes for 5456 basis states (depends on basis size and computer properties.)
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