Related papers: Inaccurate use of asymptotic formulas
The Laplace transform approach with convolution theorem is used to find the scattering phase shifts of a Mie-type potential. The normalized scattering wave functions are also studied. The bound state spectrum and the corresponding…
We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As…
A novel integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys. Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential equation…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\hat{x}_m$ are distributed so that…
We give an exact result about the asymptotic limit of an oscillatory integral whose phase contains a certain flat term. Corresponding to the real analytic phase case, one can see an essential difference in the behavior of the above…
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative…
We show that using the electric field as a quantization variable in nonlinear optics leads to incorrect expressions for the squeezing parameters in spontaneous parametric down-conversion and conversion rates in frequency conversion. This…
General equations for the calculation of amplitudes are presented. As an illustration of application of proposed formulae we calculate electron-electron scattering amplitudes.
A method of calculation of the scattering amplitude for fermions and scalar bosons with exchanging of a scalar particle in ladder approximation is suggested. The Bethe-Salpeter ladder integral equations system for the imaginary part of the…
Analytical solutions to acoustic scattering problems involving nonspherical shapes, such as spheroids and disks, have long been known and have many applications. However, these solutions require special functions that are not easily…
We give a short review of the algebraic procedure known as deformation quantisation, which replaces a commutative algebra with a non-commutative algebra. We use this framework to examine how the objects known as wavefunctions, as known in…
The scattering phase shift encodes a good amount of physical information which can be used to study resonances from scattering data. Among others, it can be used to calculate the continuum density of states and the collision time in a…
We consider the scattering of a low-frequency gravitational wave by a massive compact body in vacuum. We apply partial-wave methods to compute amplitudes for the helicity-conserving and helicity-reversing contributions to the cross section,…
Based on the invariance of the phase of waves, plane waves was shown to propagate with negative frequencies in a medium which moves at superluminal speeds opposite to the propagation direction of plane waves. The validity of the invariance…
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…
We solve the shifted wave equation \begin{align*} \frac{\partial^2}{\partial t^2}\varphi(x,t)=(\Delta_x+\rho^2)\varphi(x,t) \end{align*} on a non compact simply connected harmonic manifold with mean curvature of the horospheres $2\rho>0$.…
I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is…