Maple procedures for the coupling of angular momenta. IV. Spherical harmonics Original Research Article

Spherical harmonics play a crucial role in theoretical physics since they represent a complete and orthonormal set of functions on the unit sphere. The spherical harmonics are therefore applied in many different fields of physics including classical field theory as well as the treatment of quantum many-particle systems. Along with their well-known properties, they are frequently utilized to evaluate one- and many-particle matrix elements from atomic and nuclear structure theory analytically.In this paper, we present an extension of the Racah program to incorporate the behaviour and the properties of the spherical harmonics. Our new version also supports various useful expansions for these functions, recursion relations as well as the algebraic evaluation of integrals.