Related papers: Anharmonic oscillator and the optimized basis expa…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
The Rayleigh-Ritz procedure for determining bound-states of the Schr\"{o}dinger equation relies on spectral representation of the solution as a linear combination of the basis functions. Several possible extensions of the method to…
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these…
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients…
In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain…
We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT-symmetry of odd potentials for…
We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for…
Vibrational spectra can be computed without storing full-dimensional vectors by using low-rank sum-of-products (SOP) basis functions. We introduce symmetry constraints in the SOP basis functions to make it possible to separately calculate…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
The energy eigenvalues of the anharmonic oscillator characterized by the cubic potential for various eigenstates are determined within the framework of the hypervirial-Pad\'e summation method. For this purpose the E[3,3] and E[3,4] Pad\'e…
We introduce non conforming virtual elements to approximate the eigenvalues and eigenfunctions of the two dimensional acoustic vibration problem. We focus our attention on the pressure formulation of the acoustic vibration problem in order…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the…
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the…
We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by…
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…