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In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…

Analysis of PDEs · Mathematics 2022-12-08 Ruipeng Shen

We consider solutions to the linear wave equation on non-compact Riemannian manifolds without boundary when the geodesic flow admits a filamentary hyperbolic trapped set. We obtain a polynomial rate of local energy decay with exponent…

Analysis of PDEs · Mathematics 2007-11-19 Hans Christianson

We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a…

Analysis of PDEs · Mathematics 2025-07-23 Rémi Carles , Yavdat Ilyasov

The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…

Quantum Physics · Physics 2016-03-22 B. C. Lütfüoğlu , F. Akdeniz , O. Bayrak

In this paper, we consider the wave equation in space dimension 3 with an energy-supercritical, focusing nonlinearity. We show that any radial solution of the equation which is bounded in the critical Sobolev space is globally defined and…

Analysis of PDEs · Mathematics 2012-08-13 Thomas Duyckaerts , Carlos Kenig , Frank Merle

The wave functions and the ground state energies for the bound states of four different muonic and electronic molecules, governed by the Chern-Simons potential in two spatial dimensions, are numerically obtained with the Numerov method. The…

Quantum Physics · Physics 2023-08-22 Francisco Caruso , Vitor Oguri , Felipe Silveira , Amos Troper

We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…

Analysis of PDEs · Mathematics 2020-12-16 Rémi Carles , Clément Gallo

The Faddeev-Yakubowski equations have been solved in configuration space for the four nucleons system. Results for bound and scattering states in the isospin and S-wave approximation for different (T,S) channels are presented. The n-t…

Nuclear Theory · Physics 2009-10-31 F. Ciesielski , J. Carbonell , C. Gignoux

We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the…

Quantum Physics · Physics 2023-07-21 Farhang Loran , Ali Mostafazadeh

Partial wave theory of a two dimensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard disk'' like potential and the magnetic flux is…

Quantum Physics · Physics 2015-06-26 de-Hone Lin

In this work, inverse scattering transform for the sixth-order nonlinear Schr\"{o}dinger equation with both zero and nonzero boundary conditions at infinity is given, respectively. For the case of zero nonzero boundary conditions, in terms…

Exactly Solvable and Integrable Systems · Physics 2021-07-06 Weiqi Peng , Yong Chen

One-dimensional time-independent Schr\"odinger equation is solved for the asymmetric Hulth\'{e}n potential. Reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is…

Mathematical Physics · Physics 2011-07-19 Altuğ Arda , Oktay Aydoğdu , Ramazan Sever

Bound-state-like wave functions are used to determine the scattering matrix corresponding to low energy $N-d$ and $p-^3$He collisions. To this end, the coupled channel form of the integral relations derived from the Kohn variational…

Nuclear Theory · Physics 2015-05-30 A. Kievsky , M. Viviani , L. E. Marcucci

The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not…

Quantum Physics · Physics 2007-05-23 A. Raiteri

A brief description of the novel approach towards solving few-body scattering problems in a finite-dimensional functional space of the $L_2$-type is presented. The method is based on the complete few-body continuum discretization in the…

Nuclear Theory · Physics 2009-11-13 V. N. Pomerantsev , V. I. Kukulin , O. A. Rubtsova

We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for bound states in a basis set of finite size. We obtain two classes of solutions written as finite series of square integrable functions…

Quantum Physics · Physics 2022-08-22 A. D. Alhaidari

Scattering and transition amplitudes with three-hadron final states play an important role in nuclear and particle physics. However, predicting such quantities using numerical Lattice QCD is very difficult, in part because of the effects of…

High Energy Physics - Lattice · Physics 2015-11-17 Maxwell T. Hansen

We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations.…

Nuclear Theory · Physics 2024-01-17 V. S. Timoteo , U. van Kolck

Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…

Quantum Physics · Physics 2017-11-27 E. M. Ferreira , J. Sesma

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…

Mathematical Physics · Physics 2015-06-26 A. Amaya-Tapia , G. Gasaneo , S. Ovchinnikov , J. H. Macek , S. Y. Larsen