Matrix elements of a many‐particle hamiltonian evaluated using hyperspherical coordinates

Two formulas derived in previous articles are used to evaluate the matrix elements of a general many‐particle Hamiltonian. The first formula is an expansion of the Coulomb potential of the system in terms of hyperspherical harmonics, while the second is a general formula for the evaluation of angular integrals in many‐dimensional spaces. These two formulas lead to explicit expressions for the Hamiltonian matrix elements when the basis functions are mononomials in the 3 N coordinates multiplied by functions of the hyperradius.