Recovery of a 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 {E_j,s_j}, where E_j are the bound states energies and s_j are the values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem -u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0, \infty) norm. An algorithm is given for recovery of p(r) from few experimental data.