© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

The Journal of Chemical Physics

Quantum theory of large amplitude vibrational motions in a one-dimensional Morse chain

Byung Chan Eu

Published Sep 1, 1980• 6 citations

Abstract

By introducing appropriately generalized annihilation and creation operators for oscillators interacting by Morse potentials and generalized coherent states, we have derived the quantal equations of motion for displacements in a one-dimensional chain of Morse oscillators. The equations of motion derived have the same mathematical structures as their classical analogs which have been studied before. Since they are essentially identical in structure, it is possible to infer from the classical studies that the quantal system also would exhibit solitary waves and solitons. It is pointed out in the paper that the formalism used here for anharmonic systems should also be useful for other fields of study related to high amplitude vibrational motions of polyatomic molecules for which the usual normal mode analysis is not suitable.

DOI: 10.1063/1.440390

Related papers

Vibrational coherent states for Morse oscillator

N.M. Avram, G. E. Drăgănescu, Calin N. Avram

For the one-dimensional Morse oscillator we have built a set of creation and annihilation operators and established the corresponding coherent states. The average values of some observables in these coherent states have been calculated and their time evolution established. In order to study the strong vibrations of di-atomic molecules we use a three-dimensional Morse oscillator model and its dynamic group. For this system we have built the coherent states and calculated the dynamic modifications of the refractive index of the molecules, as the result of interaction with a laser beam.

Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2000•15 citations

Model ofncoupled generalized deformed oscillators for vibrations of polyatomic molecules

Dennis Bonatsos A, C. Daskaloyannis

A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed through the use of quantum-algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss [Phys. Rev. Lett. 66, 2976 (1991)], suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscillators. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown.

Physical Review A•Nov 1, 1993•37 citations

Coupled Q-oscillators as a model for vibrations of polyatomic molecules

Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis

The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

arXiv:quant-ph/9701025•The Journal of Chemical Physics•Jan 8, 1997•30 citations

Generalized and Gaussian coherent states for the Morse potential

Maia N Angelova, Véronique Hussin

In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1 H 35 Cl.

Journal of Physics A Mathematical and Theoretical•Jul 15, 2008•44 citations

Coupled Q-oscillators as a model for vibrations of polyatomic molecules

Dennis Bonatsos A, Daskaloyannis, C, Kolokotronis, P

The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the $Q$-oscillators by deformed anharmonic oscillators. The generalization to $n$ oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

•Jan 1, 1996•21 citations

A simple algebraic approach to coherent states for the Morse oscillator

Ian L. Cooper

Minimum uncertainty coherent states and annihilation operator coherent states for the Morse oscillator are derived and shown to be equivalent. They reduce, in the limit of small anharmonicity constant, or, equivalently, in the limit of large well depth, to the approximate coherent states derived previously from the use of generalized displacement operator.

Journal of Physics A Mathematical and General•Mar 21, 1992•55 citations

By introducing appropriately generalized annihilation and creation operators for oscillators interacting by Morse potentials and generalized coherent states, we have derived the quantal equations of motion for displacements in a one-dimensional chain of Morse oscillators. The equations of motion derived have the same mathematical structures as their classical analogs which have been studied before. Since they are essentially identical in structure, it is possible to infer from the classical studies that the quantal system also would exhibit solitary waves and solitons. It is pointed out in the paper that the formalism used here for anharmonic systems should also be useful for other fields of study related to high amplitude vibrational motions of polyatomic molecules for which the usual normal mode analysis is not suitable.

For the one-dimensional Morse oscillator we have built a set of creation and annihilation operators and established the corresponding coherent states. The average values of some observables in these coherent states have been calculated and their time evolution established. In order to study the strong vibrations of di-atomic molecules we use a three-dimensional Morse oscillator model and its dynamic group. For this system we have built the coherent states and calculated the dynamic modifications of the refractive index of the molecules, as the result of interaction with a laser beam.

A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed through the use of quantum-algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss [Phys. Rev. Lett. 66, 2976 (1991)], suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscillators. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown.

The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the suQ(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.

In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1 H 35 Cl.

The system of two

Q

-deformed oscillators coupled so that the total Hamiltonian has the su

_Q

(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the

Q

-oscillators by deformed anharmonic oscillators. The generalization to

n

oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.