Construction of coherent states for Morse potential: A su(2)-like approach

Belfakir, Abdessamad; Hassouni, Y.; Curado, Evaldo M. F.

doi:10.1016/j.physleta.2020.126553

Cited by 13 publications

(6 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…By means of the canonical transformation (x, p) → (x γ , Πγ ), the asymmetric deformed oscillator with PDM is mapped into a Morse oscillator, and the coherent states for the latter are well known. Coherent states for the Morse oscillator were previously investigated in different approaches: minimum-uncertainty, 66 Perelomov generalized definition, 67 time dilatation operator, 68 algebraic method, 69 Gazeau-Klauder and Barut-Girardello approaches, 70,71 generalized and Gaussian coherent states, 72 generalized Heisenberg algebra and su(2)-like approach, 73 etc.…”

Section: Coherent States and Minimum Relation Of Uncertaintymentioning

confidence: 99%

“…We have limited this work in investigating Glauber's coherent states for the deformed oscillator. However, the investigation of generalized coherent states for systems with PDM can be obtained from the approaches of Klauder and Sudarshan, 3-5 Barut and Girardello, 6,71 Gazeau-Klauder, 70 and Perelomov, 7,67 quantum anomaly in the systems with the second order supersymmetry, 65 generalized Heisenberg algebras, 73 and conformal quantum mechanical 76 in interesting additional developments. A group theoretical approach to the deformed oscillator, including both bound and scattering, can be obtained in future developments from the formalism introduced in Ref.…”

Section: Dynamics Of Quasi-classical Statesmentioning

confidence: 99%

See 1 more Smart Citation

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

da Costa,

Gomez,

Rath

2023

Preprint

View full text Add to dashboard Cite

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (x γ , Π γ ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

show abstract

Section: Coherent States and Minimum Relation Of Uncertaintymentioning

confidence: 99%

Section: Dynamics Of Quasi-classical Statesmentioning

confidence: 99%

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

da Costa,

Gomez,

Rath

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…If the dissociation energy is known, the first-type approximation makes it possible to obtain the frequency values and wave functions of the states in a wider range, but with somewhat less accuracy. Add that just this approach was long before and widely used in the theoretical study of the dynamic interaction of strong laser radiation with matter, when pumping over the vibrational degrees of freedom of the molecule occurs up to dissociation and transition to a continuous spectrum [16][17][18]. In these cases, it is more important to know the dissociation energy more accurately than the ordering law of the eigenfrequencies of the anharmonic oscillator.…”

Section: Alternative Approximations Of the Real Electronic Termmentioning

confidence: 99%

Implementation of Morse potential for approximation of vibrational terms of diatomic molecules

Denisov

Tokhadze

2022

Optics and Spectroscopy

View full text Add to dashboard Cite

We analysed the problem of approximation of the potential function of a diatomic molecule by a Morse model function with constant anharmonicity ν x using the Birge-Sponer extrapolation. The analysis of the approximations used in the derivation of the Morse equation shows that the solution of this problem is ambiguous. A scheme for optimizing the selection of initial parameters is proposed, which is illustrated by examples taken from the literature. The advantages of delineation of anharmonicity in the excitation of vibrational levels by deviations of the value ν x from the constant value according to Morse are demonstrated. An attempt is made to use the dimensionless anharmonicity parameter x* as a universal characteristic of the shape features of the electronic term of the molecule. Keywords: Morse potential, diatomic molecule, Birge-Sponer extrapolation, anharmonicity, electronic terms, vibrational structure.

show abstract

“…Если же энергия диссоциации известна, аппроксимация первого типа позволяет получить значения частот и волновые функции состояний в более широком интервале, но с несколько меньшей точностью. Добавим, что именно этот подход давно и широко используется при теоретическом изучении динамического взаимодействия сильного лазерного излучения с веществом, когда происходит накачка по колебательным степеням свободы молекулы вплоть до диссоциации и перехода в сплошной спектр [16][17][18]. В этих случаях более важно точнее знать энергию диссоциации, чем закон упорядоченности собственных частот ангармонического осциллятора.…”

Section: альтернативные аппроксимации реального электронного термаunclassified

Возможности Формулы Морза При Аппроксимации Энергии Колебательных Уровней Двухатомной Молекулы

Денисов¹,

Тохадзе²

2021

Оптика И Спектроскопия

View full text Add to dashboard Cite

Рассмотрена задача аппроксимации потенциала двухатомной молекулы модельной функцией Морза с постоянной ангармоничностью ν x при использовании экстраполяции Берджа-Шпонер. Анализ приближений, использованных при выводе уравнения Морза, показывает, что решение этой задачи неоднозначно. Предложена схема оптимизации выбора исходных параметров, которая иллюстрирована примерами, взятыми из литературы. Продемонстрирована польза изучения поведения ангармоничности при возбуждении колебательных уровней по отклонениям величины ν x от постоянного значения по Морзу. Предпринята попытка использовать безразмерный параметр ангармоничности x* в качестве универсальной характеристики особенностей формы электронного терма молекулы. Ключевые слова: формула Морза, двухатомная молекула, экстраполяция Берджа-Шпонер, ангармоничность, электронные термы, колебательная структура.

show abstract

Construction of coherent states for Morse potential: A su(2)-like approach

Cited by 13 publications

References 39 publications

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

Implementation of Morse potential for approximation of vibrational terms of diatomic molecules

Возможности Формулы Морза При Аппроксимации Энергии Колебательных Уровней Двухатомной Молекулы

Contact Info

Product

Resources

About