INVERSE SPECTRAL PROBLEM FOR ATOM-LIKE MESONS
D. U. MatrasulovDepartment of Heat Physics, Uzbek Academy of Sciences, 28 Katartal St., 700135 Tashkent, UzbekistanZ. A. SobirovDepartment of Heat Physics, Uzbek Academy of Sciences, 28 Katartal St., 700135 Tashkent, UzbekistanK.K. SabirovDepartment of Heat Physics, Uzbek Academy of Sciences, 28 Katartal St., 700135 Tashkent, Uzbekistan
ABI
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 = 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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