Van Vleckの吸収の対応原理とKramersの分散理論

概要

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The quantum theory formula of dispersion was first proposed by H. A. Kramers in 1924, in the period of the old quantum theory. As is well known, he obtained the classical formula by applying the perturbation theory to the multiply periodic system and then transformed it into the quantum formula by replacing the differential quotients by the difference quotients. This replacement is the first generalization of the correspondence principle for frequencies. However, Kramers was not the only one. J. H. Van Vleck almost at the same time conceived the same idea of replacement and applied it to the different matter : the correspondence principle for absorption of radiation by atoms. He defined the "differential" absorption energy as the increment obtained by subtracting the energy of induced emission from the true absorption energy, and confirmed that it is this differential absorption that corresponds to the classical absorption. Kramers' dispersion formula consists of the positive and negative terms of the classical type. The negative term, however, could not be derived from the classical differential equation based on the oscillator model. Nevertheless, if one accepts the virtual oscillator model and replaces the classical absorption by the differential absorption (Eq. [29] in the text), then two terms may be obtainable without using the multiply periodic system and the perturbation method.
日本科学史学会の論文
1993-06-25