Related papers: Variational Methods for Path Integral Scattering
This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…
A non-stationary method for tunneling description of non-relativistic particles and photons through a barrier on the basis of consideration of the multiple internal reflections of vawe packets in relation of barrier boundaries is presented.…
The simulation of light scattering by particles on a substrate with the $T$-matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an…
A giant atom is an artificial matter configuration whose spatial scale is comparable to the wavelength of the interacting electromagnetic wave, such that the usual electric-dipole approximation is no longer valid. As a consequence, certain…
We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational…
Electromagnetic scattering and absorption by material particles is a fundamental physical problem with a broad range of applications, going from laboratory experiments, biology and material sciences, all the way up to environmental studies…
Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the $L^2$ transition probability amplitude. We will do this for nonvector potential Hamiltonians with potential…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We report on the development of a systematic variational perturbation theory for the euclidean path integral representation of the density matrix based on new smearing formulas for harmonic correlation functions. As a first application, we…
This work extends previous results on the inverse scattering problem within the framework of Marchenko theory (fixed-$l$ inversion). In particular, I approximate an $n$-channel $S$-matrix as a function of the first-channel momentum $q$ by a…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…
In this paper we present some open problems pertaining to the approximation theory involved in the solution of the important class of Nonlinear Partial Differential Equations (NPDEs) of integrable type. For this class of NPDEs, any Initial…
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying classical (minimal Euclidean action) path, to be referred to…
We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical…