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Canadian Journal of Physics

Creation and annihilation operators for the Morse oscillator and the coherent states

G. E. Drăgănescu, N.M. Avram

Published Jan 1, 1998• 7 citations
Publisher

Abstract

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DOI
10.1139/cjp-76-4-273

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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.
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.
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.