Recovery of Quarkonium System from Experimental Data

For confining potentials of the form q(r) = r+ p(r), where p(r) decays rapidly and is smooth for r > 0, it is proved that q(r) can be uniquely recovered from the data {Ej , sj}∀j=1,2,3..... Here Ej are energies of bound states and sj are the values u ′ j(0), where uj(r) are the normalized eigenfunctions, ∫∞ 0 u 2 jdr = 0. An algorithm is given for finding q(r) from the knowledge of few first data, corresponding to 1 ≤ j ≤ J assuming that the rest of the data are the same as for q0(r) := r.