Orbital excitations of the charmonium and bottomium levels in the statistical model

The statistical model has been extended to deal with orbital excitations like the P and D states of the psi(cc-bar) and Υ(bb-bar) families. The wave functions suggested by the statistical model, when used as inputs into the corresponding Schroedinger wave equation as trial functions, yield reasonably accurate values of the masses of the lowest S, P, and D levels in the psi and Υ families. The corresponding virial theorem is also found to be satisfied exactly for the harmonic oscillator potential and to high order of accuracy for the corresponding linear-potential case