相关论文: The Relativistic Linear Singular Oscillator
This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…
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…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
Nonlinear Schr\"odinger (NLS) equations with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator…
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…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and momentum operators of the oscillator as odd elements of the Lie…
We construct one dimensional exactly solvable model by choosing a probe fundamental string rotating and pulsating in the planar Lifshitz spacetime that follows nonrelativistic Lifshitz scaling. We present suitable sets of embedding…
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the non-relativistic bound state energy spectrum E_{n} and the wave functions…
The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different…
Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
In this article we study the problem of a non-relativistic particle in the presence of a singular potential in the noncommutative plane. The potential contains a term proportional to $1/R^2$, where $R^2$ is the squared distance to the…