# Anharmonic Oscillator

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### Alexander V Turbiner – 1st expert on this subject based on the ideXlab platform

• ##### radial AnharmonicOscillator perturbation theory new semiclassical expansion approximating eigenfunctions ii quartic and sextic Anharmonicity cases
International Journal of Modern Physics A, 2020
Co-Authors: J C Del Valle, Alexander V Turbiner

Abstract:

In our previous paper I (del Valle–Turbiner, 2019) a formalism was developed to study the general D-dimensional radial Anharmonic Oscillator with potential V (r) = 1 g2 V(gr). It was based on the …

• ##### radial AnharmonicOscillator perturbation theory new semiclassical expansion approximating eigenfunctions i generalities cubic Anharmonicity case
International Journal of Modern Physics A, 2019
Co-Authors: J C Del Valle, Alexander V Turbiner

Abstract:

For the general D-dimensional radial Anharmonic Oscillator with potential V (r) = 1 g2 V(gr) the perturbation theory (PT) in powers of coupling constant g (weak coupling regime) and in inverse, fr…

• ##### AnharmonicOscillator and double well potential approximating eigenfunctions
Letters in Mathematical Physics, 2005
Co-Authors: Alexander V Turbiner

Abstract:

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical Anharmonic Oscillator and the double-well potential given by V=m2x2+gx4 at arbitrary g ≥ 0 for m2>0 and m2<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory

### Sameer M Ikhdair – 2nd expert on this subject based on the ideXlab platform

• ##### dirac bound states of AnharmonicOscillator 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 AnharmonicOscillator 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 – 3rd expert on this subject based on the ideXlab platform

• ##### quantum versus classical dynamics in a periodically driven AnharmonicOscillator
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