By using the formalism ofsecond quantization and irreducible tensor,quasispin angular momentum scalaroperator Z(K),where K=2,…,2j,is constructed from 4 creation-annihilation operators.Theeigenvalues of Z(K) have special ability for classification of coupled states,by angular momentum J and quasispin Q the complete classification can be done only for j≤7/2,but by eigenvalues of Z(K)the complete classification have be donefor j≤15/2.The methods for calculating the eigenvalues of Z(K)are discussed,and the complete classifications for j≤15/2 are presented.

Four numerical methods for calculating coefficients of fractional parentage(CFP) of nucleons are compared,and the results show that the method of complete space by neutron-proton couplied is much better than that of over complete space,the method of factorization by group chains is much better than that of non factorization,and there are great differences of calculating amonut between different methods.

Visualization In Scientific Computing (VISC) is a rapidly developing application of computer graphics. This paper introduces a Visualization System In Quantum Mechanics-VISQUM, and discusses some methods and techniques used in this system.

According to the group chain[SO(5)⊃U(1)_DⓧSU(2)_T]ⓧ[Sp(2j+1)⊃O(3)],the coupling states of j-shell nucleons are classified by D=(n-2 j-1)/2,isospin T,angular momentum J and generalized quasispin[s,t],where s is generalized siniority and t is reduced isospin;the multiplicities classified are products of SO(5)⊃U(1)_DⓧSU(2)_T and Sp(2j+1)⊃O(3) group reduction multiplicities.The explicit formulas for the two group reduction multiplicities are presented,and some results calculated are listed.

A bisection method is presented for solving the eigenvalue problem of symmetric band matrices.This method is especially suitable for the case where only a few eigenpairs are needed. Further more,a modified strategy is also presented.The main idea is that firstly using the bisection for some steps to obtain an approximate eigenvalue,then Rayleigh Quotient Iteration is applied to extract the eigenvalue to a predifined accuracy.