Practicing the Correspondence Principle in the Old Quantum Theory by Martin Jähnert

Author:Martin Jähnert
Language: eng
Format: epub
ISBN: 9783030133009
Publisher: Springer International Publishing

Without addressing how such a relation could be understood on the basis of the core idea of the correspondence principle, Kramers stipulated, the continuous classical spectrum could be connected with the discrete set of spectral lines. This association allowed him to determine the intensity of the X-ray line from the integral intensity of a range of frequencies ν + dν in the cut-off part of the spectrum. In the graphical representation shown in Fig. 5.4, the area corresponding to the cut-off part of the classical spectrum was transformed into the area corresponding to the spectral line. Somehow, it seems, the classical intensity should be concentrated around the frequency of the spectral line. Building on this speculation, Kramers used his description of the classical spectrum to determine the transition probability for bound-free transitions and finally arrived at a value for the absorption cross section.

Fig. 5.4Kramers’ qualitative representation of the continuous spectrum in Kramers (1923, 855)

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