Related papers: Perturbation-based Non-perturbative Method
We give a brief overview of a simple and unified way, called the prepotential approach, to treat both exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation. It is based on the prepotential together with Bethe…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are…
This paper presents a new method for solving a class of nonlinear optimal control problems with a quadratic performance index. In this method, first the original optimal control problem is transformed into a nonlinear two-point boundary…
Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be…
We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient,…
Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on…
The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…
We describe three different methods for generating quasi-exactly solvable potentials, for which a finite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions;…
We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic,…
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential…
In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenvalue result is well known to a broad…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…
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…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using…