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We consider matrix structures in the quantum N-body problem that generalize the Faddeev components for resolvents, T-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of T-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators. [ABSTRACT FROM AUTHOR]

The 2D problem of diffraction of a plane wave by a periodically irregular perfectly conducting surface is solved with the help of the null-field method. Comparative analysis of the computation accuracy is performed for various techniques of choosing an auxiliary contour on which the null-field condition is imposed. It is shown that the choice of an auxiliary contour based on the analytical deformation of the surface contour is an optimal technique. [ABSTRACT FROM AUTHOR]

The T-matrix method is modified with the use of a priori information on the analytic properties of a solution. It is shown that taking into account such information makes it possible to develop correct, effective, and universal algorithms for simulating scattering characteristics of bodies of a wide class of geometries including essentially non-Rayleigh bodies. [ABSTRACT FROM AUTHOR]

The screening limit of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann–Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values. [ABSTRACT FROM AUTHOR]

The article elaborates solution to the Parquet Equations for a Two-Matrix Model. The vacuum energy and correlation functions were calculated for the Hermitian zero-dimensional single matrix model. The planar-parquet approximation was also suggested. Considering the symmetric form of the potential, a truncated system of planar-parquet equations for the propagators is analyzed to present a numerical solution. It is concluded that these two approaches are in good agreement.

A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-α-particle model interacting via the deep αα potential by Buck, Friedrich, and Wheatley is investigated. [ABSTRACT FROM AUTHOR]

We formulate quantum scattering theory in terms of a discrete L2-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: S- and T-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann-Schwinger equations for the T-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators. [ABSTRACT FROM AUTHOR]