A method based on a nonlinear generalized Heisenberg algebra to study the molecular vibrational spectrum

Souza, Jeferson de; Oliveira-Neto, N. M.; Ribeiro-Silva, C. I.

doi:10.1140/epjd/e2006-00155-6

Cited by 14 publications

(16 citation statements)

References 46 publications

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“….) are very close, ensuring that the finite parts of the partition functions of equations (8) and (22) are approximately the same.…”

Section: Analysis Of the Energy Spectrum Of A Special Q-oscillatormentioning

confidence: 98%

“…Recently, a generalization of the Heisenberg algebra was constructed [20,21], which contains the q-oscillator algebra as a particular case. This generalized Heisenberg algebra can be used also as a simple model for describing phenomenologically the energy spectrum of more complicated composite particles (for an application of such an approach to the CO molecule, see [22]).…”

Section: Analysis Of the Energy Spectrum Of A Special Q-oscillatormentioning

confidence: 99%

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A simple model to describe the low-temperature behaviour of some atoms and molecules: an application to the hydrogen atom

Oliveira-Neto

Curado

Nobre

et al. 2007

J. Phys. B: At. Mol. Opt. Phys.

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A simple model to describe the low-temperature behaviour of some atoms and molecules is proposed and applied to the hydrogen atom. To this end, the low-temperature dynamics of the approach to equilibrium of the hydrogen atom is analysed by means of a standard Monte Carlo simulation. It is shown that, before approaching ionization, the atom may live for a long time in a quasi-equilibrium state whose duration increases exponentially for decreasing temperatures. Essentially, this effect is directly related to the low probability associated with the transition between the ground-and first-excited states, which demands an enormous amount of energy (75% of the whole energy spectrum). Therefore, for low temperatures, the atom may take a long time to overcome such an energy barrier. It is argued that the dynamical behaviour associated with the approach to equilibrium of some composite particles, characterized by an energy spectrum presenting an upper bound, preceded by the accumulation of an infinite number of levels-for which the hydrogen atom represents a prototype-can be described, at low temperatures, by a special class of q-oscillators. By suitably adjusting the deformation parameter q, characteristic of these q-oscillator systems, one obtains a dynamical behaviour at low temperatures which resembles that associated with the composite particle of interest. In order to reproduce the results of the hydrogen atom, the central idea is that this parameter may be set to a value, in such a way that the energy gap between the ground-and first-excited states coincide in the two systems. The method is illustrated by choosing q = 1/4, in which case one gets a remarkable agreement, from both qualitative and quantitative points of view, with the dynamical behaviour of the hydrogen atom. The conditions of applicability of the method are discussed.

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“….) are very close, ensuring that the finite parts of the partition functions of equations (8) and (22) are approximately the same.…”

Section: Analysis Of the Energy Spectrum Of A Special Q-oscillatormentioning

confidence: 98%

Section: Analysis Of the Energy Spectrum Of A Special Q-oscillatormentioning

confidence: 99%

A simple model to describe the low-temperature behaviour of some atoms and molecules: an application to the hydrogen atom

Oliveira-Neto

Curado

Nobre

et al. 2007

J. Phys. B: At. Mol. Opt. Phys.

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show abstract

“…An algebraic structure which contains q-oscillators as a particular case was proposed in ] and has been successfully used in some different physical problems [Oliveira-Neto et al(2007), de Souza et al(2006), Bezerra,Curado,Rego-Monteiro(2002), Ribeiro-Silva,Curado,Rego-Monteiro(2008), Curado,Rego-Monteiro(2006), ]. In this new algebra, called Generalized Heisenberg Algebra (GHA), the commutation relations among the operators a, a † and a diagonal operator J 0 which is going to replace in the present context x N introduced in (100) depend on a general functional h(x) and are given by: J 0 a † = a † h(J 0 ) (104)…”

Section: Generalized Heisenberg Tripletmentioning

confidence: 99%

Noncommutative reading of the complex plane through Delone sequences

Ali

Balkova

Curado

et al. 2009

Journal of Mathematical Physics

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The Berezin-Klauder-Toeplitz ("anti-Wick") quantization or "non-commutative reading" of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction properties of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on the natural numbers. This work is an attempt for following the same path by considering sequences of non-negative numbers which are not "too far" from the natural numbers. In particular, we examine the consequences of such perturbations on the non-commutative reading of the complex plane in terms of its probabilistic, functional, and localization aspects.

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“…It is well-known that the topic of rotational and molecular vibrational spectroscopy is one of the essential areas of molecular physics and it can be counted as one of the main implements for other scientific areas such as environmental sciences [21] and biology [1]. However, the harmonic oscillator could be served as a background to describe the molecular vibrations [22]. However, to improve the theory of molecular vibrations the anharmonic oscillators can be applied to solve exactly the Schrodinger equation and provide more reliable model for diatomic molecules [23].…”

Section: Introductionmentioning

confidence: 99%

Quantum pseudodots under the influence of external vector and scalar fields

Eshghi

Ikhdair

2018

Chinese Phys. B

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We study the spherical quantum pseudodots in the Schrodinger equation using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility and the persistent currents are also studied using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.

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A method based on a nonlinear generalized Heisenberg algebra to study the molecular vibrational spectrum

Cited by 14 publications

References 46 publications

A simple model to describe the low-temperature behaviour of some atoms and molecules: an application to the hydrogen atom

A simple model to describe the low-temperature behaviour of some atoms and molecules: an application to the hydrogen atom

Noncommutative reading of the complex plane through Delone sequences

Quantum pseudodots under the influence of external vector and scalar fields

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