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

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 Ykαi (Ωi) 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 Ykαi (Ωi) to other set such as Ykαi (Ωj. 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.