Comment on “The Bohr-Sommerfeld Theory and the Uncertainty Principle”

T. Tietz

Yatendra Pal Varshni

Jagdish Mehra, Helmut Rechenberg

Robert Yaris

Yardley Beers

It is suggested that, if the Wilson-Sommerfeld quantization postulate is modified such that phase integrals for nonignorable coordinates are placed equal to half-integers times Planck's constant while those for ignorable coordinates are placed equal to integers times Planck's constant, eigenvalues that are in much better agreement with quantum mechanics are obtained. Also there results a picture of the radiation process that is conceptually consistant with classical theory. It avoids the picture of an electron making many revolutions in a closed orbit without radiating. Some of the discussion is based upon developments in classical theory that have evolved since the Bohr-Sommerfeld theory was formulated. In addition, some of the effects of the uncertainty principle are made more apparent.

Gilbert Chin

Before the Heisenberg-Schrödinger formulation of quantum mechanics, the semiclassical Bohr-Sommerfeld theory successfully accounted for quantized properties such as the energy levels in the hydrogen atom. However, the forcing of closed orbits for particle motion ran afoul of the uncertainty principle. Recently, the use of Dscaling, in which the motion of each particle is described by a vector in D dimensions, was used to reintroduce the uncertainty principle to this earlier theory. When properly done, such equations reduce to the correct Schrödinger form for D = 3 but can still be solved in the more tractable D→ ∞ limit. This D scaling approach was applied successfully to atoms but did not yield bound states for molecules.