INVERSE SPECTRAL PROBLEM FOR ATOM-LIKE MESONS

Abstract

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 = I2 is multiplicative identity matrix, it is proved that q(x) in the Dirac equation can be uniquely recovered from the data {λj, sj}. Here λj are the eigenvalues of the Dirac equation and sj are the values yj(0) = (sj, 0) T , where yj(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 q0(x):= 0, m = 0 is proposed.