Related papers: Perturbed Poeschl-Teller oscillators
A simple algebraic technique is developed to obtain deformed energy spectra for the P\"oschl-Teller potentials.
We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [3]. The…
Nonspherical perturbation theory has been necessary to understand the meaning of radiation in spacetimes generated through fully nonlinear numerical relativity. Recently, perturbation techniques have been found to be successful for the time…
Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
We consider the weak turbulence of whistler waves in the in low-\beta\ inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering…
We analyze the one dimensional scattering produced by all variations of the P\"oschl-Teller potential, i.e., potential well, low and high barriers. We show that the P\"oschl-Teller well and low barrier potentials have no resonance poles,…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states…
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…
A variation of the valence electron wave function inside a nucleus induced by a perturbative potential is expressed in terms of the potential momenta. As an application we consider QED vacuum polarization corrections due to the Uehling and…
We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobolev norms. We use these modulated bubbles of energy to…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with the inverse linear dispersion law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave number, and…
Particle-in-cell code, EPOCH, is used for studying features of the wave component evident to propagate backwards from the front of the non-gyrotropic, relativistic beam of electrons injected in the Maxwellian, magnetised background plasma…
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 present a procedure that allows the construction of the metric perturbations and electromagnetic four-potential, for gravitational and electromagnetic perturbations produced by sources in Kerr spacetime. This may include, for example,…
This work derives a variant of the perturbed convective wave equation based on the acoustic perturbation equations for compressible flows. In particular, the derivation reformulates the relation of Helmholtz's decomposition to the acoustic…