The motion of bodies in power‐law potentials of the form V(r)=λrα has been of interest ever since the time of Newton and Hooke. Aspects of the relation between powers α and ᾱ, where (α+2)(ᾱ+2)=4, are derived for classical motion and the relation to the quantum‐mechanical problem is given. An improvement on a previous expression for the WKB quantization condition for nonzero orbital angular momenta is obtained. Relations with previous treatments, such as those of Newton, Bertrand, Bohlin, Fauré, and Arnold, are noted, and a brief survey of the literature on the problem over more than three centuries is given.

Topics
Operator theory, Quantization condition
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© 1994 American Association of Physics Teachers.
1994
American Association of Physics Teachers
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