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We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
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…
A novel self-consistent implementation of Hedin's GW perturbation theory is introduced. This finite-temperature method uses Hartree-Fock wave functions to represent Green's function. GW equations are solved with full potential linear…
In this paper we provide a new technique to find solutions to the Klein-Gordon-Maxwell system. The method, based on an iterative argument, permits to improve previous results where the reduction method was used. We also show how this device…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
An analysis shows that the ground state of the inhomogeneous system of interacting electrons in the static external field, which satisfies the thermodynamic limit, can be consistently described only using the Green function theory based on…
The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of…
We consider one-dimensional Fokker-Planck and Schr\"odinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be…
The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $\delta$-function central barrier. We find solutions that have the symmetry of the non-interacting…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
The double-layer potential plays an important r$\hat{\rm o}$le in solving boundary value problems of elliptic equations. Here, in this paper, we aim at introducing and investigating double layer potentials for a generalized bi-axially…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
The notion of non-perturbative renormalization is discussed and extended. Within the extended picture, a new non-perturbative representation for the generating functional of Green functions of quantum field theories is suggested. It is…
We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the…
A two-dimensional electron system interacting with an impurity and placed in crossed magnetic and electric fields is under investigation. Since it is assumed that an impurity center interacts as an attractive $\delta$-like potential a…
Unique transformation properties under the hyperspherical inversion of a partial differential equation describing a stationary scalar wave in an $N$-dimensional ($N\geqslant2$) Maxwell fish-eye medium are exploited to construct a closed…
In the recent paper [J.\ Phys.\ A 44 (2011) 065203], we have arrived at the closed-form expression for the Green's function for the partial differential operator describing propagation of a scalar wave in an $N$-dimensional ($N\geqslant2$)…
We present a method to determine the impurity Greens function of the interacting resonant level model (IRLM) using numerical simulation techniques based on the expansion of a resolvent expression in terms of Chebyshev polynomials. The…
This paper proposes a new gradient method to solve the large-scale problems. Theoretical analysis shows that the new method has finite termination property for two dimensions and converges R-linearly for any dimensions. Experimental results…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…