PERIODIC SYSTEMS OF MOLECULES FROM GROUP THEORY
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Date
1993
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Publisher
Ohio State University
Abstract
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 $li > = b^{+}\, _{i}lo>$ correspond to various atoms where $lo>$ is the vacuum state vector, and $b^{+}_{j}$ is the creation operator for atom i. The annihilation operator is $b_{1}$; boson symmetry requires $[b_{i},b_{j}] = [b^{+}\, _{i}b^{+}_{j}] = 0, |b_{i}b^{+}_{i}| = 1$. 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 $\Sigma_{i,i} Pl(ij) b^{+}_{i}b_{j}$. 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.
Description
Author Institution: Department of Physics, Southern College; Department of Physics, St. Petersburg University