Related papers: Comment on: "The asymptotic iteration method revis…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
In this comment we show that the approach presented by Foj\'on et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which…
This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymptotic formulas for the mean square errors of the filtering…
In this paper [published in Phys. Rev. E 102, 042210 (2020)], a new method for the calculation of excited chaotic eigenfunctions in arbitrary energy windows is presented. We demonstrate the feasibility of using wavefunctions localized on…
In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…
In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility.
We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the…
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in…
In this note we point out that results on the asymptotic behaviour of an alternative iterative method are corollaries of corresponding results on the well-known Halpern iteration.
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…
Recent work has shown a deep connection between semilocal approximations in density functional theory and the asymptotics of the sum of the WKB semiclassical expansion for the eigenvalues. However, all examples studied to date have…
We argue that the claimed optimality of a new process tomography method suggested in [quant-ph/0601033] and [quant-ph/0601034] is based on not completely fair comparison that does not take into account the available information in an equal…
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…
In this paper we show that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model. It consists of an eigenvalue…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
We review recent results on the existence of asymptotic observables in algebraic QFT. The problem of asymptotic completeness is discussed from this perspective.
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
Here we revisit the quantum phase estimation (QPE) algorithm, and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with…