Anharmonic Oscillator

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Alexander V Turbiner - One of the best experts on this subject based on the ideXlab platform.

Sameer M Ikhdair - One of the best experts on this subject based on the ideXlab platform.

  • dirac bound states of Anharmonic Oscillator in external fields
    Annals of Physics, 2014
    Co-Authors: Majid Hamzavi, Sameer M Ikhdair, B J Falaye
    Abstract:

    Abstract We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector Anharmonic Oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.

  • an alternative simple solution of the sextic Anharmonic Oscillator and perturbed coulomb problems
    International Journal of Modern Physics C, 2007
    Co-Authors: Sameer M Ikhdair, R Sever
    Abstract:

    Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic Anharmonic Oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic Anharmonic Oscillator problem with eigenvalue $\hat E$. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with k = D +2l appearing in the wave equation satisfy certain constraints.

H J Korsch - One of the best experts on this subject based on the ideXlab platform.

  • quantum versus classical dynamics in a periodically driven Anharmonic Oscillator
    Physical Review A, 1992
    Co-Authors: N Bental, Nimrod Moiseyev, H J Korsch
    Abstract:

    Numerical studies of the classical and quantum dynamics of a periodically driven Anharmonic Oscillator show that the only quasienergy states that are exponentially localized in the field-free energy space are those that ared located in the regular region of classical phase space. All the quasienergy states located in the bounded chaotic region in the phase space are extended states and do not show the strong quantum limitation of chaos due to the Anderson localization mechanism, which is characteristic of kicked systems

Robert Conte - One of the best experts on this subject based on the ideXlab platform.

  • Partial integrability of the Anharmonic Oscillator
    Journal of Nonlinear Mathematical Physics, 2008
    Co-Authors: Robert Conte
    Abstract:

    We consider the Anharmonic Oscillator with an arbitrary-degree Anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g1(x) u' + g2(x) u + g3(x) u^n + g4(x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing Oscillator and numerous dynamical systems. The present work is an overview which includes and generalizes all previously known results of partial integrability of this Oscillator. We give the most general two conditions on the coefficients under which a first integral of a particular type exists. A natural interpretation is given for the two conditions. We compare these two conditions with those provided by the Painleve' analysis.

  • partial integrability of the Anharmonic Oscillator
    Journal of Nonlinear Mathematical Physics, 2007
    Co-Authors: Robert Conte
    Abstract:

    We consider the Anharmonic Oscillator with an arbitrary-degree Anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u ′′ + g1(x)u ′ + g2(x)u + g3(x)u n + g4(x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing Oscillator and numerous dynamical systems. The present work is an overview which includes and generalizes all previously known results of partial integrability of this Oscillator. We give the most general two conditions on the coefficients under which a first integral of a particular type exists. A natural interpretation is given for the two conditions. We compare these two conditions with

Carl M. Bender - One of the best experts on this subject based on the ideXlab platform.

  • multiple scale analysis of the quantum Anharmonic Oscillator
    Physical Review Letters, 1996
    Co-Authors: Carl M. Bender, Luis M A Bettencourt
    Abstract:

    Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical Anharmonic Oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum Anharmonic Oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.

  • Anharmonic Oscillator ii a study of perturbation theory in large order
    Current Physics–Sources and Comments, 1990
    Co-Authors: Carl M. Bender, Tai Tsun Wu
    Abstract:

    This paper is concerned with the nature of perturbation theory in very high order. Specifically, we study the Rayleigh-Schrodinger expansion of the energy eigenvalues of the Anharmonic Oscillator. We have developed two independent mathematical techniques (WKB analysis and difference-equation methods) for determining the large- n behavior of A K n , the n th Rayleigh-Schrodinger coefficient for the K th energy level. We are not concerned here with placing bounds on the growth of A K n , as n , the order of perturbation theory, gets large. Rather, we consider the more delicate problem of determining the precise asymptotic behavior of A K n , as n → ∞ for both the Wick-ordered and non-Wick—ordered Oscillators. Our results are in exact agreement with numerical fits obtained from computer studies of the Anharmonic Oscillator to order 150 in perturbation theory.