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A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities…

Analysis of PDEs · Mathematics 2021-02-16 Johan Helsing , Andreas Rosén

We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection…

High Energy Physics - Theory · Physics 2023-07-24 David Berenstein , George Hulsey

We study the scattering problem, the Sturm-Liouville problem and the spectral problem with periodic or skew-periodic boundary conditions for the one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic) potential. We give…

Mathematical Physics · Physics 2007-05-23 Piotr G. Grinevich , Roman G. Novikov

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently…

High Energy Physics - Phenomenology · Physics 2015-06-05 Pierpaolo Mastrolia , Edoardo Mirabella , Giovanni Ossola , Tiziano Peraro

We construct a scattering matrix with operator valued entries describing solutions to the 1+1 wave equation where permittivities has memory and depends on time and space. It is the analogue of the scattering matrix for spatially localised…

Analysis of PDEs · Mathematics 2026-02-24 Jeffrey Galkowski , Zhen Huang , Maciej Zworski

Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related…

Spectral Theory · Mathematics 2009-11-07 A. Volberg , P. Yuditskii

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…

Quantum Physics · Physics 2009-11-10 A. D. Alhaidari

The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…

High Energy Physics - Theory · Physics 2019-07-22 Robert M. Schabinger

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…

Mathematical Physics · Physics 2023-07-31 Tadayoshi Adachi , Yuta Tsujii

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is…

Quantum Physics · Physics 2024-10-18 Giuseppe Mussardo , Andrea Stampiggi , Andrea Trombettoni

It is known that the Jost-function formulation of quantum scattering theory can be applied to classical problems concerned with the scattering of a plane scalar wave by a medium with a spherically symmetric inhomogeneity of finite extent.…

Classical Physics · Physics 2014-05-14 Umaporn Nuntaplook , John A Adam

We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…

Quantum Physics · Physics 2020-09-14 A. D. Alhaidari

We point out little discussed phenomenon in elementary quantum mechanics. In one-dimensional potential scattering problems, the scattering amplitudes are not uniquely determined at special points in parameter space. We examine a few…

Quantum Physics · Physics 2021-12-15 Makoto Natsuume , Takashi Okamura

Multiple scattering of polarised electromagnetic waves in diffusive media is investigated by means of radiative transfer theory. The method becomes exact in several situations of interest, such as a thick-slab experiment (slab thickness L…

Condensed Matter · Physics 2009-10-28 E. Amic , J. M. Luck , Th. M. Nieuwenhuizen

As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two…

Quantum Physics · Physics 2009-11-07 B. Demircioglu , S. Kuru , M. Onder , A. Vercin

A method to construct multi-indexed exceptional Laguerre polynomials using isospectral deformation technique and quantum Hamilton-Jacobi (QHJ) formalism is presented. We construct generalized superpotentials using singularity structure…

Mathematical Physics · Physics 2017-11-15 S. Sree Ranjani

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…

Numerical Analysis · Mathematics 2022-04-01 Carlos Jerez-Hanckes , Ignacio Labarca

In this paper, we construct a Darboux transformation (DT) of the (2+1)-dimensional Schr\"odinger-Maxwell-Bloch equation (SMBE) which is integrable by the Inverse Scattering Method. Using this DT, the one-soliton solution and periodic…

Exactly Solvable and Integrable Systems · Physics 2014-02-20 G. Shaikhova , K. Yesmakhanova , G. Mamyrbekova , R. Myrzakulov

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

Analysis of PDEs · Mathematics 2023-06-21 Jian Zhai , Yue Zhao