The Bohr-Sommerfeld Theory and the Uncertainty Principle

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.