Bohr-Sommerfeld quantization and meson spectroscopy

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Abstract
We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulas for the energy spectra which closely approximate numerical exact calculations performed with the Schrödinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables such as the rms radius or wave function at the origin. The asymptotic dependence of these observables on quantum numbers is also obtained in the case of potentials which behave asymptotically as a power law. We discuss the constraints imposed by these formulas on the dynamics of the quark-antiquark interaction.
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