Atomik üç cisim problemi

It is possible to solve the Schrödinger equations of some quantum mechanical many-body system exactly in hyperspherical coordinates. One solution to this equation is the Fock expansion of the total wave function of the system in the neighborhood of r=0. Another method is to expand the wave function into a series for an orthonormal complete basis set of generalized Laguerre polynomials, L_n^ν, and hyperspherical harmonic functions, Y_λμ (Ω). After obtaining the reduction relations, the matrix form is proceeded and the secular determinant is constructed for non-trivial solutions. The energy eigenvalues are obtained by solving this determinant depending on the energy parameter ξ.