Properties of Velocity-Dependent Potentials

Ferreira, E.; Guillén, Nilo; Sesma, J.

doi:10.1063/1.1705149

Cited by 9 publications

(2 citation statements)

References 19 publications

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“…Classical and quantum momentum-or velocity-dependent Hamiltonian systems have been extensively studied in the literature over many decades mainly due to their relevant, wide and varied physical applications. Without trying to be exhaustive, let us mention that linear momentum-dependent Hamiltonians have been considered from different viewpoints in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and quadratic momentum-dependent ones have been analysed in [16][17][18][19][20]. In addition, exponentials of momentum-dependent potentials (V ∝ e − p 2 ) have also been considered in [21][22][23][24] and another more involved momentum-dependent potential was recently introduced in [25]; see references therein in all the aforementioned works.…”

Section: Introductionmentioning

confidence: 99%

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

2023

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We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by where q i and p i are generic canonical variables, γ n are arbitrary coefficients, and N ∈ N . For N = 2, being both γ 1 , γ 2 different from zero, this reduces to the classical Zernike system. We prove that always provides a superintegrable system (for any value of γ n and N) by obtaining the corresponding constants of the motion explicitly, which turn out to be of higher-order in the momenta. Such generic results are not only applied to the Euclidean plane, but also to the sphere and the hyperbolic plane. In the latter curved spaces, is expressed in geodesic polar coordinates showing that such a new superintegrable Hamiltonian can be regarded as a superposition of the isotropic 1 : 1 curved (Higgs) oscillator with even-order anharmonic curved oscillators plus another superposition of higher-order momentum-dependent potentials. Furthermore, the symmetry algebra determined by the constants of the motion is also studied, giving rise to a ( 2 N − 1 ) th-order polynomial algebra. As a byproduct, the Hamiltonian is interpreted as a family of superintegrable perturbations of the classical Zernike system. Finally, it is shown that (and so the Zernike system as well) is endowed with a Poisson s l ( 2 , R ) -coalgebra symmetry which would allow for further possible generalizations that are also discussed.

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Section: Introductionmentioning

confidence: 99%

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

2023

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“…The properties of the Schr€ odinger equation including velocity-dependent potential and the singularities of the corresponding differential equation were studied in order to probe properties of velocity-dependent potential and it was found that there is a simple agreement between the velocitydependent problem and a static one. 1 The velocity-dependent potential was first considered in order to investigate the scattering of mesons from the complex nuclei. 2 Also, the velocity-dependent potential was used to model nucleonnucleon interaction and reproduced the 1 S; 1 D; 1 G singleteven phase shift.…”

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confidence: 99%

Plasma screening effects on the energies of hydrogen atom under the influence of velocity-dependent potential

Bahar

2014

Physics of Plasmas

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In order to examine the plasma screening and velocity-dependent potential effects on the hydrogen\ud atom, the Schr€odinger equation including a more general exponential cosine screened Coulomb and\ud velocity-dependent potential is solved numerically in the framework asymptotic iteration method.\ud The more general exponential cosine screened Coulomb potential is used to model Debye and quantum\ud plasma for the specific values of the parameters in its structure. However, in order to examine\ud effects of velocity-dependent potential on energy values of hydrogen atom in Debye and quantum\ud plasma, the isotropic form factor of velocity-dependent potential is given as harmonic oscillator type,\ud qðrÞ ¼ qor2. Then, the energies of s and p states are calculated numerically without any approximation.\ud In order to investigate thoroughly plasma screening effects and contribution of velocitydependent\ud potential on energy values of hydrogen atom, the corresponding calculations are carried\ud out by using different values of parameters of more general exponential cosine screened Coulomb\ud potential and isotropic dependence, results of which are discusse

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On the low-energy scattering by velocity-dependent potentials

Sesma

Vento

1977

Lett. Nuovo Cimento

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Properties of Velocity-Dependent Potentials

Cited by 9 publications

References 19 publications

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

Plasma screening effects on the energies of hydrogen atom under the influence of velocity-dependent potential

On the low-energy scattering by velocity-dependent potentials

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