A theorem on the order of levels in confining potentials |
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Authors: | A Martin |
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Institution: | CERN, Geneva, Switzerland |
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Abstract: | We prove that in a two-body, non-relativistic system interacting via a potential V = ?g2/r + Vc(r), where Vc is a confining potential non-singular at the origin, the 2S level is above the 2P level if Vc satisfies the following sufficient condition: This covers the well-known cases of linear potentials or harmonic oscillator potentials, which were considered in charmonium models, but also more generally, for instance, Vc(r) = rα, α >0. |
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