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On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle. Part one

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Abstract

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, USA

    Anthony Duncan

  2. Program in the History of Science, Technology, and Medicine, University of Minnesota, Minneapolis, USA

    Michel Janssen

  3. Tate Laboratory of Physics, 116 Church St. NE, Minneapolis, MN, 55455, USA

    Michel Janssen

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  1. Anthony Duncan
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  2. Michel Janssen
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Correspondence to Michel Janssen.

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Communicated by J.D. Norton.

This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.

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Duncan, A., Janssen, M. On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle. Part one. Arch. Hist. Exact Sci. 61, 553–624 (2007). https://doi.org/10.1007/s00407-007-0010-x

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