Calculation of Energy Eigenvalues and Eigenvectors for Three Body Molecules in Jacobi and Hyperspherical Coordinates

Journal Article · Thu Aug 13 04:00:00 EDT 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3225425· OSTI ID:21317002

Eskandari, M R; Khajehazad, H ^[1]

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1. Physics Department, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of)

The jacobi coordinates is used to eliminate center of mass motion of three body systems. We write the results in hyperspherical coordinates and expand eigenfunction in a series of orthonormal complete set of Y{sub k{alpha}{sub i}} ({omega}{sub i}) in partition i of jacobi coordinates. The matrix elements of two body interaction potential in hyperspherical harmonic approach are determined exactly using computed analytical form of Raynal-Revai coefficients to change the base set of Y{sub k{alpha}{sub i}} ({omega}{sub i}) to other set such as Y{sub k{alpha}{sub i}} ({omega}{sub j}. The generalized Laguerre functions are used to change the second order coupled differential equations to set of non-differential matrix equation. This is solved to find energy eigenvalues and eigenfunctions of three body molecules. The obtained analytical results are in a very good agreement with used computational method.

• OSTI ID: 21317002
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1148; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BINDING ENERGY
EIGENFUNCTIONS
EIGENVALUES
EIGENVECTORS
MATRICES
MATRIX ELEMENTS
MOLECULES
POTENTIALS
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
TWO-BODY PROBLEM