ATOMIC ANALOGUES OF PROBLEMS INVOLVING THE COUPLING OF ANGULAR MOMENTA IN MOLECULES
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Date
1951
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Ohio State University
Abstract
Klein has observed that, when referred to axes mounted on the molecular framework, the components of a molecule's total angular momentum satisfy the usual commutation rules, but with an anomalous sign of i. On the other hand, the components of ``internal'' (spin or orbital electronic) angular momentum satisfy these rules with he normal sign. As Nielsen has pointed out, the negatives or ``reverses'' of the internal angular momentum will satisfy them with the same anomalous sign as the total angular momentum. When quantities to be compounded are similar in their commutation behavior, the relations for the addition of angular momentum vectors given in Condon and Shortley, etc., can be used. However, because of the fact that the reverse of the internal angular momentum must be used, addition in the atomic case corresponds to subtraction in the molecular one. When this modification is taken into account, it can be shown that to practically every secular problem involving the coupling to angular momenta in molecules there is a mathematically similar one in atoms, when allowance is made for the difference in notation. Although the analogy is only a formal one, it facilitates the formulation of secular problems in atoms, since most physicists are more familiar with atomic than molecular quantization, and since texts such as Condon and Shortley's threat atomic coupling in great detail. Our extension of Klein's theory enables us to use such texts to obtain matrix elements in various systems of quantization (cases a,b,etc.) in molecular problems.
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Author Institution: Department of Physics, Harvard University