The Physical Pendulum in Quantum Mechanics
It is pointed out that the Mathieu functions of even order are the characteristic functions of the physical pendulum in the sense of Schrödinger’s wave mechanics. The relation of various properties of the functions, as known from purely analytical investigations of them, to the pendulum problem is discussed.
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- 1.An account of them is given in Whittaker and Watson, A Course of Modern Analysis, Chap. 19 (1920). This is, however, quite incomplete now because of the many more recent investigations by British and Scottish mathematicians.Google Scholar
- 2.See e.g. Goldstein, Trans. Cambr. Phil. Soc. 23, 303, (1927) Par. 1.5. This memoir contains a good many of the newer results not given in Whittaker and Watson.Google Scholar
- 3.Jeffreys, Proc. London Math. Soc. 23, 437, (1924–25). This paper and the one preceding it are especially interesting in that the methods of approximate integration which he uses are closely related to those by means of which the connection between classical mechanics and quantum mechanics is established.MATHCrossRefGoogle Scholar