Three-particle integrals with the Bessel functions

TL;DR

This paper derives analytical formulas for complex three-particle integrals involving Bessel and trigonometric functions, facilitating calculations in quantum mechanics and related fields.

Contribution

It introduces new analytical formulas for three-particle integrals with Bessel and trigonometric functions, enabling more complex integral evaluations.

Findings

Formulas applicable to integrals with interparticle coordinates

Facilitates calculations of matrix elements in quantum problems

Enables analysis of more complicated functions of relative coordinates

Abstract

Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas obtained in such an analysis allow us to consider three-particle integrals of more complicated functions of relative/perimetric coordinates. In many actual problems such three-particle integrals can be found in matrix elements of the Hamiltonian and other operators.