Macrocosmos/microcosmos: celestial mechanics and old quantum theory |
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Authors: | Steven N. Shore |
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Affiliation: | a Department of Physics and Astronomy, Indiana University South Bend, 1700 Mishawaka Ave, South Bend, IN 46634-7111, USA;b Department of Physics, University of Pisa, via Buonarroti 2, 56127, Pisa, Italy |
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Abstract: | The Bohr atom was a solar system in miniature. Despite many deep foundational questions related to the origin of quantized motion, rapid progress was made in its mathematical development and its apparently successful application to spectral line series. In United States, where celestial mechanics flourished throughout the 19th and well into the 20th century, mathematicians and physicists were well prepared for just this sort of problem and made it their own far faster than many areas of the new physics. This paper examines the link between classical problems of perturbation theory, three-body and N-body orbital trajectories, the Hamilton–Jacobi equation, and the old quantum theory. I discuss why it was comparatively easy for American applied mathematicians, astronomers, and mathematical physicists to make significant contributions quickly to quantum theory and why further progress toward quantum mechanics by the same cohort was, in contrast, so slow. |
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Keywords: | Celestial mechanics Hamilton– Jacobi equations History of mathematics and mathematicians, 20th century Quantum theory, historical |
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