Related papers: The propagator for the step potential using the pa…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to V_{q}(r) a…
Using a scheme proposed earlier we set up Hamiltonian path integral quantization for a particle in two dimensions in plane polar coordinates.This scheme uses the classical Hamiltonian, without any $O(\hbar^2)$ terms, in the polar…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
Starting from well-known expressions for the $T$-matrix and its derivative in standard nonrelativistic potential scattering I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow…
Exact path integration for the one dimensional potential $V=b^2\cos 2q$ which describes the finite amplitude pendulum is presented.
We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a…
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials, which were…
We study some distributive lattices arising in the combinatorics of lattice paths. In particular, for the Dyck, Motzkin and Schroder lattices we describe the spectrum and we determine explicitly the Euler characteristic in terms of natural…
Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals…
Although Potent purports to use only radial velocities in retrieving the potential velocity field of galaxies, the derivation of transverse components is implicit in the smoothing procedures. Thus the possibility of using nonradial line…
In this work, we propose a novel framework for accelerating the parareal algorithm, in which the coarse propagator is formulated as a two-step method and optimized with respect to the convergence factor.} We derive a rigorous error estimate…
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
Darboux transformations of the singular harmonic oscillator are considered. Analytical expressions for the propagators are obtained, using the image method applied to formal singular propagators. Two-well and three-well families of…
We use the factorization method to find the exact eigenvalues and eigenfunctions for a particle in a box with the delta function potential $V(x)=\lambda\delta(x-x_{0})$. We show that the presence of the potential results in the…
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length,…
We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label…
We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving…