Abstract
An extension of the solution of the inversion problem reproducing the potentials and wave functions from the given singularities of the Jost functions on a static limit relativistic case of theS-wave Klein-Gordon equation is investigated by way of the method elaborated by Petráš in Czech. J. Phys.B12 (1962), 67. It is shown that similarly as in the non-relativistic case, a transparent representation of the relativistic Jost solution permits to determine uniquely the potentials decreasing exponentially at large distances and leads to the dispersive Fredholm integral equations for the Jost solution components. The proposed method might be considered as an alternative to that used by Cornille in J. Math. Phys.11 (1970), 79.
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Weiss, J. Relativistic jost functions and potentials. Czech J Phys 21, 1019–1031 (1971). https://doi.org/10.1007/BF01690915
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DOI: https://doi.org/10.1007/BF01690915