On the verge of \textit{Umdeutung} in Minnesota: Van Vleck and the correspondence principle. II. (Q2460937)

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On the verge of \textit{Umdeutung} in Minnesota: Van Vleck and the correspondence principle. II.
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    On the verge of \textit{Umdeutung} in Minnesota: Van Vleck and the correspondence principle. II. (English)
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    19 November 2007
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    In this second part we present the detailed derivations on which our narrative in the first part rests (see the review Zbl 1129.01008 above). The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking that led to Heisenberg's \textit{Umdeutung} paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr's correspondence principle to construct their quantum counterparts both for the special case of charged harmonic oscillator and for arbitrary nondegenerate multiply-periodic system. We then rederive these results in modern quantum mechanics. Bibliography consists of 63 items, of which 13 are new with respect to part one.
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    Heisenberg's Umdeutung paper
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    Bohr's correspondence principle
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