Symbolic Algorithm for Generating the Orthonormal Bargmann–Moshinsky Basis for $$\mathrm {SU(3)}$$ Group

Abstract

A symbolic algorithm which can be implemented in any computer algebra system for generating the Bargmann–Moshinsky (BM) basis with the highest weight vectors of \(\mathrm {SO(3)}\) irreducible representations is presented. The effective method resulting in analytical formula of overlap integrals in the case of the non-canonical BM basis [S. Alisauskas, P. Raychev, R. Roussev, J. Phys. G 7, 1213 (1981)] is used. A symbolic recursive algorithm for orthonormalisation of the obtained basis is developed. The effectiveness of the algorithms implemented in Mathematica 10.1 is investigated by calculation of the overlap integrals for up to \(\mu =5\) with \(\lambda > \mu \) and orthonormalization of the basis for up to \(\mu =4\) with \(\lambda > \mu \). The action of the zero component of the quadrupole operator onto the basis vectors with \(\mu =4\) is also obtained.