arXiv subjects
Publications and source records attributed to Vagner Jikia.
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used in quantum mechanics of two charged particles of a continuous spectrum.
We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.
A correct high-energy asymptotic form of Faddeev type few-body integral equations is found. Iterative series corresponding to these asymptotic relations converge with a certain accuracy to a finite sum, which satisfies the corresponding condition of unitarity.
It is well known that multi-particle integral equations of collision theory, in general, are not compact. At the same time it has been shown that the motion of three and four particles is described with consistent integral equations. In particular, by using identical transformations of the kernel of the Lipman-Schwinger equation for certain classes of potentials Faddeev obtained Fredholm type integral equations for three-particle problems $[1]$. The motion of for bodies is described by equations of Yakubovsky and Alt-Grassberger-Sandhas-Khelashvili $[2.3]$, which are obtained as a result of two subsequent transpormations of the kernel of Lipman-Schwinger equation. in the case of $N>4$ the compactness of multi-particle equations has not been proven yet. In turn out that for sufficiently high energies the $N$-particle $\left( {N \ge 3} \right)$ dynamic equations have correct asymptotic solutions satisfying unitary condition $[4]$. In present paper by using the Heitler formalism we obtain the results briefly summarized in Ref. [4]. In particular, on the bases of Heitler's equation [5] a unitary asymptotic solution of the system of $N$-particle scattering integral equations is found, which represents a generalization to any number of particles of the result of Ref. $[6]$ obtained for three particles.