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Love and physics: Margrethe Nørlund and Niels Bohr's creativity ...

Love and physics: Margrethe Nørlund and Niels Bohr's creativity ...

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Helge Kragh, University of Aarhus, Denmark<br />

The Many Faces of the Bohr Atom<br />

The atomic model that Bohr proposed in 1913 constituted a break with all earlier models of the atom.<br />

However, the break was not complete, for it relied in important respects on the approach of J. J.<br />

Thomson <strong>and</strong> others. Nor was the new picture of the atom fixed. Bohr conceived it as preliminary <strong>and</strong><br />

immediately started developing <strong>and</strong> modifying it. There is a great deal of difference between the Bohr<br />

atom anno 1913 <strong>and</strong> the one of 1924, although there are also significant similarities.<br />

Apart from some remarks of a historiographical nature, my talk offers a general survey of the<br />

development of Bohr’s theory, stressing its relationship to experiments. I intend to evaluate its<br />

significance, both in the scientific communities (<strong>physics</strong>, chemistry) <strong>and</strong> in a broader context. Apart<br />

from the original theory, I will pay particular attention to the “second theory” of 1921-1923 <strong>and</strong> the<br />

much less visualizable version of 1924-1925. Finally, I will take a look beyond 1925, wondering if<br />

Bohr’s theory is truly dead. Perhaps it is, like Schrödinger’s poor cat, half dead <strong>and</strong> half alive?<br />

Michiyo Nakane, Kawasaki, Japan<br />

Bohr’s Introduction to Action-Angle Variables in a 1918 Paper<br />

Action-angle variables provide one of the most important mathematical techniques for quantum theory.<br />

These variables originated in Charlier’s books on celestial mechanics published in 1902 <strong>and</strong> 1907.<br />

Charlier performed a canonical transformation defined by a particular generating function <strong>and</strong> attained<br />

new canonical variables constructed by angle variables <strong>and</strong> action integrals. Noting Charlier’s<br />

argument, Schwarzschild defined action-angle variables <strong>and</strong> used them for an explanation of Stark<br />

effects in 1916. However, he did not present action variables in the form of Ii=∫pidqi, but he noted<br />

variables that have the same dimension as the action integrals that construct canonical variables<br />

together with angle variables, ωi=nit+βi, where t is time, ni is the mean motion, <strong>and</strong> βi is the initial<br />

value of the angle. In a 1918 paper entitled “On the Quantum Theory of Line-Spectra,” Bohr mentioned<br />

that Kramers showed him a way to make Ii <strong>and</strong> ωi canonical conjugates. An origin of formation of<br />

action-angle variables that we find in textbooks of mechanics today first appeared here. Then, Bohr<br />

developed his idea of a conditionally periodic system using the action variables Ii.<br />

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