INVERSE SPECTRAL PROBLEM FOR ATOM-LIKE MESONS

Inverse spectral problem for the Dirac equation with quark–antiquark potential is treated. For a class of potentials of the form Q(x) = q(x) E + (m + x)I, where q(x) = o(1) for x → +∞, [Formula: see text], E = I 2 is multiplicative identity matrix, it is proved that q(x) in the Dirac equation can be uniquely recovered from the data {λ j , s j }. Here λ j are the eigenvalues of the Dirac equation and s j are the values y j (0) = (s j , 0) T , where y j (x) are the normalized eigenfunctions of the Dirac Hamiltonian, [Formula: see text]. An algorithm for finding q(x) from the known first few data, corresponding to -J ≤ j ≤ J assuming that the rest of the data are the same as for q 0 (x):= 0, m = 0 is proposed.

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