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International Journal of Quantum Chemistry

Coherent states for anharmonic diatomic molecules

J. Récamier, P. García de León, Rocío Jáuregui, Alejandro Frank, Octavio Castaños

Published Jan 1, 2002• 14 citations
Publisher

Abstract

Abstract In this work, we construct approximate coherent states for a Morse‐like potential using the displacement operator method and a method recently proposed by Gazeau and Klauder. To test if these states are minimum uncertainty states, we evaluate the temporal evolution of the dispersions in position and momentum. We also construct the trajectories in the phase space and compare with the classic solution. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

DOI
10.1002/qua.10322

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Abstract In this work, we construct approximate coherent states for a Morse‐like potential using the displacement operator method and a method recently proposed by Gazeau and Klauder. To test if these states are minimum uncertainty states, we evaluate the temporal evolution of the dispersions in position and momentum. We also construct the trajectories in the phase space and compare with the classic solution. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
We construct a deformed oscillator whose energy spectra is similar to that of a Morse potential. We obtain a convenient algebraic representation of the displacement and the momentum of a Morse oscillator by expanding them in terms of deformed creation and annihilation operators and we compute their average values between approximate coherent states of the deformed oscillator, and we compare them to the results obtained using the exact Morse coordinate and momenta. Finally we evaluate the temporal evolution of the dispersion (Δx)(Δp) and show that these states are not minimum uncertainty states.
The generalization of the concept of coherent states for a Morse potential based on the real or complex displacements of the equilibrium position of the ground-state wave function yields a natural framework for their generation via Franck-Condon transitions. We study the relevance of including continuum states in the proper treatment of these displaced states, particularly for the description of their time evolution. It is shown that displaced Morse states may exhibit mathematical and physical temporal stability manifested through the presence of revivals in spite of the unbound character of the included continuum states. The Wigner function of these states is presented as well as relations to previous constructions. The time evolution of particular phase space properties such as mean values of position and momentum as well as their uncertainties are also analyzed.
We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.
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.
Abstract We analyze the response of a single anharmonic diatomic molecule to a monochromatic time dependent electric field ω(t) and evaluate the temporal evolution of the dipole moment, phase space trajectories, and several transition probabilities as a function of the intensity of the field. We define deformed boson operators A† = f( )a†, A = af( ) in terms of the usual harmonic oscillator creation and annihilation operators a, a†, = a†a and choose the number operator function f( ) such that the energy spectrum of a harmonic oscillator‐type Hamiltonian written in terms of the deformed operators yields an energy spectrum similar to that of a Morse potential. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005