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

On generation of the Bargmann-Moshinsky basis of SU(3) group

“…was described in [11] and implemented as a symbolic algorithm in [12]. Let us introduce the notation for overlaps of the vectors of this basis:…”

“…The number L max is determined in a similar manner. An illustrative example for calculation of allowed values of α and L is presented in Table 1 of ref [12]. It should be noted that the set of allowed values of L for overlap integrals is given by intersection of these sets for the corresponding < bra| and |ket > vectors.…”

“…Then we expand the vectors (12) in the terms of basis (17). As the first step we apply the multipliers of ( 12) in the variables ξ −1 , ξ 0 , ξ 1 , η −1 , η 0 , η 1 .…”

“…We start from the BM states which are linearly independent but as in other approaches not orthonormal. We developed an effective symbolic algorithm suitable for implementation in computer algebra systems [12]. It is based on the adapted Gram-Schmidt orthonormalization procedure but using the overlap integrals calculated in an analytical form [11].…”

“…These calculations do not involve any square root operation. This distinct features of the proposed orthonormalization algorithm allows for a large scale symbolic calculations [12].…”