Recovery of a quarkonium system from experimental data
Abstract
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, where Ej are the bound states energies and sj are the values of u'j(0), and uj(r) are the normalized eigenfunctions of the problem -uj" +q(r)uj=Ejuj, r>0, uj(0)=0, ||uj||=1, where the norm is L2(0, ∞) norm. An algorithm is given for recovery of p(r) from few experimental data.
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