The semiclassical Wentzel–Kramers–Brillouin (WKB) method applied to one-dimensional problems with bound states often reduces to the Sommerfeld–Wilson quantization conditions, the cyclic phase-space integrals

. It turns out that this formula gives the exact bound-state energies for the Morse oscillator with

. The requisite integral can be reduced to

, in which

and

are the classical turning points

. The integral can be done "by hand", using the transformation

followed by a contour integration in the complex plane, but

*Mathematica* can evaluate the integral explicitly, needing only the additional fact that

The result reads

, which can be solved for

to give

,

, in units with

. The highest bound state is given by

, where

represents the floor, which for positive numbers is simply the integer part. The values of

,

, and

(expressed in atomic units) used in this Demonstration are for illustrative purposes only and are not necessarily representative of any actual diatomic molecule.