Related papers: Diffraction in the Semiclassical Approximation to …
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…
This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
We study the quantum slit diffraction problem in three dimensions. In the treatment of diffraction of particles by a slit, it is usually assumed that the motion perpendicular to the slit is classical. Here we take into account the effect of…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
Semiclassical expansions for traces involving Greens functions have two contributions, one from the periodic or recurrent orbits of the classical system and one from the phase space volume, i.e. the paths of infinitesimal length.…
We introduce a classical fractional particle model in $\mathbb{R}^{n}$, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
We introduce the semiclassical limit to electronic systems by taking the limit $\hbar\rightarrow 0$ in the solution of Schr\"odinger equations. We show that this limit is closely related to one type of strong correlation that is…
The problem of a Dirac particle moving in a deformed Hulthen potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green's function of…
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…
For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…
The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's…