"Periodic Systems of Moiecules from Group Theory" by R. Cavanaugh, Ray Hefferlin et al.
 

Document Type

Article

Publication Date

1993

Abstract

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+ ~o> correspond to various atoms where lo> is the vacuum state vector, and b+i is the creation operator for atom i. The annihilation operator is b;; boson symmetry requires fbrbJ = b+ rb+ J = 0, [bi,b+ j] = 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 I:i,j P1(i;j) b+pj" 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.

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