Knowledge Bank

We assume that atoms are indistinguishable particles which can be transformed one into another by the elements of a group $G.1$ which corresponds to the internal symmetry of their periodic system. We construct a molecular periodic system using G and bosonic creation operators. The vectors $li>=b+ilo>$ correspond to various atoms where $lo>$ is the vacuum state vector, and $bj+$ is the creation operator for atom i. The annihilation operator is $b1$; boson symmetry requires $[bi,bj]=[b+ibj+]=0,|bibi+|=1$. State vectors $lijk..>$ correspond to molecules. They can be recast as a direct sum of irreducible representations whose vectors are (often) linear combinations of individual molecular states. The one particle operator P1 of the lie algebra of G is $\Sigma i,iPl(ij)bi+bj$. We have tested our systems by plotting a variety of tabulated experimental data along principle axes for atomic and for diatomic and triatomic molecular multiplets. I. Zhuvikin, G.V., Hefferlin, R., Vestnik Leningradskovo Universiteta No. 16, Pg. 10, 1983.