Related papers: A multiple scattering theory approach to solving t…
We present scattering from many body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…
We show that Wronskians between properly chosen linearly independent solutions of the Schr\"odinger equation greatly facilitate the study of quantum scattering in one dimension. They enable one to obtain the necessary relationships between…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
An approximate method is proposed to solve position dependent mass Schr\"odinger equation. The procedure suggested here leads to the solution of the PDM Schr\"odinger equation without transforming the potential function to the mass space or…
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…
The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Nonequiaxed inhomogeneities can lead to anisotropic wave velocity and…
Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schr\"odinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
A time-dependent statistical description of multiple particle breakage is presented. The approach combines the Tsallis non-extensive entropy with a fractal kinetic equation for the time variation of the number of fragments. The obtained…
In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the…
This paper proposes a new multiple-scattering frequency-time hybrid (FTH-MS) integral equation solver for problems of wave scattering by obstacles in two dimensional space, including interior problems in closed cavities and problems…
In this paper, the tunnelling of a particle through a potential barrier is investigated in the presence of a time-dependent perturbation. The latter is attributed to the process of the energy measurement of the scattered particle. The…
The proper time of an observer can be introduced as a degree of freedom in quantum cosmology, additional to the existing fields. We review two arguments for using the Schr\"odinger equation to evolve the corresponding wavefunction. We…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
We consider the three-dimensional cubic nonlinear Schr\"odinger system \begin{equation*} \begin{cases} i\partial_tu+\Delta u+(|u|^2+\beta |v|^2)u=0,\\ i\partial_tv+\Delta v+(|v|^2+\beta |u|^2)v=0. \end{cases} \end{equation*} Let $(P,Q)$ be…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear…
We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable…