The large distance behavior of weakly bound three-body systems is investigated. The Schr odinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of e ective radial equations are then derived. Both twoand three-body asymptotic behavior are possible and their relative importance is st...

The one-dimensional Schrodinger equation is considered when the potential and its rst moment are absolutely integrable. The transmission coe cient vanishes at zero energy in the generic case, and it never vanishes in the exceptional case. It is shown that any nontrivial exceptional potential can always be fragmented into two generic potentials. Furthermore, any nontrivial potential, generic or...

A fundamental postulate of quantum mechanics states that a measurement of a quantum system causes the collapse of the wave function. This is in contrast to the smooth, continuous, deterministic time evolution of the wave function in between measurements, governed by the Schrodinger equation. The latter is similar to classical physics; the former is unique to quantum mechanics. (Note that many ...

This article presents a relational formalization of axiomatic set theory, including socalled ZFC and the anti-foundation axiom (AFA) due to P. Aczel. The relational framework of set theory provides a general methodology for the fundamental study on computer and information sciences such as theory of graph transformation, situation semantics and analysis of knowledge dynamics in distributed syst...

Optical turbulence, which develops in the transverse directions when a laser beam propagates through a medium, is considered in the framework of the two-dimensional Schrodinger equation with a weak cubic nonlinearity. This classical model of optical turbulence was studied by many authors, but stationary (Kolmogorov) spectra that transfer transverse energy of the waves from large spatial scales...

This paper reviews the latest advances in the area of multi-soliton complexes (MSCs). We present exact analytical solutions of coupled nonlinear Schr odinger equations, which describe multi-soliton complexes and their interactions on top of a background in media with self-focusing or self-defocusing Kerr-like nonlinearities. We present numerical examples illustrating the remarkable properties ...

The performances of absorbing boundary conditions (ABCs) in four widely used finite difference time domain (FDTD) methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schr dinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave pack...