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The simplest possible nonrelativistic many‐channel p ‐wave S matrix which is meromorphic on its energy Riemann surface, as well as the underlying potential matrix, is explicitly constructed by means of the many‐channel Marchenko equations. The results suggest that, contrary to the case in...
A method for solving a restricted class of nonlinear equations is presented and applied in detail to solution of the Hartree–Fock (HF) equations.
For the inviscid eddy motion in a finite‐dimensioned Fourier space, it is stated that energy and enstrophy are the isolating constants of motion for the 2D homogeneous turbulence. In contrast, the 3D isotropic turbulence has energy as the only constant of motion. If we relax the reflexional...
The general solution of the Einstein field equation is obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure p , equal to energy density ρ, (2) the space–time is cylindrically symmetric, and (3) the metric is given by three functions of...
The l =0 partial wave projected Coulomb off‐shell T matrix T c , l =0 in momentum representation is obtained in closed form. Problems existing in the literature concerning the half‐ and on‐shell behavior of T c and T c , l are discussed and clarified by means of explicit formulas. The...
The canonical formalism for nonlinear relativistic classical field theory is presented. It is shown that the solutions Φ ( x ) of the nonlinear equation (☒+ m 2 ) Φ ( x ) =λΦ 3 ( x ) as well as the asymptotic fields Φ in ( x ) and Φ out ( x ) are local relativistic fields with respect to...
The Lorentz–Dirac equation of motion for the electron is derived by a new method which makes tedious power series expansions unnecessary.
The purpose of this article is to present a detailed analysis on the quantum mechnical level of the canonical transformation between coordinate‐momentum and number‐phase descriptions for systems possessing an s l (2, R ) dynamical algebra, specifically, the radial harmonic oscillator and...
We consider a class of possible (i.e., not known a p r i o r i to be unitary) nonrelativistic many‐channel S matrices meromorphic on their energy Riemann surfaces whose general form is suggested by the inverse scattering problem. These possible S matrices are associated with n (spinless)...
It was established by Levi‐Civita that in n dimensions there exist n +1 types of coordinate systems in which the Hamilton–Jacobi equation is separable, n of which are in general nonorthogonal; the form of the separated equations was given by Burgatti and Dall’Acqua. In this paper first the...
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