Sommerfeld—Wilson equation

In the formulation of quantum rules the characteristic of the motion which always enters explicitly is its periodicity. The only sense in which a particle executing translational motion can be said to have a period is in relation to its impacts on the sides of a containing vessel. If the particle moves parallel to the a -axis, in a cubical box of side it repeats its motion each time it completes a path of length 2Zj.. We might try using this fact to determine a periodic time insertion in the Sommerfeld-Wilson equation. 

The Wilson-Sommerfeld quantum rules, in terms of the polar coordinates r, d, and [Pg.39]

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