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Canadian Journal of Physics

Article

G. E. Drăgănescu, N.M. Avram

Published Apr 1, 1998• 0 citations
Publisher

Abstract

This paper presents the dynamic algebra of the Morse oscillatorusing a new analytic method for the calculation of creation andannihilation operators. The coherent states for the Morse potential corresponding todifferent representations are also established. The transitionsprobabilities between two eigenstates produced by a harmonicperturbation as function of the creation and annihilation operatorsare also calculated.PACS Nos.: 02.20.+b, 03.65.Fd, 42.50.Ar, and 33.10.Cs

DOI
10.1139/p97-055

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Canadian Journal of Physics•Jan 1, 1998•7 citations
This paper presents the dynamic algebra of the Morse oscillatorusing a new analytic method for the calculation of creation andannihilation operators. The coherent states for the Morse potential corresponding todifferent representations are also established. The transitionsprobabilities between two eigenstates produced by a harmonicperturbation as function of the creation and annihilation operatorsare also calculated.PACS Nos.: 02.20.+b, 03.65.Fd, 42.50.Ar, and 33.10.Cs
A realization of the raising and lowering operators for the Morse potential is presented. We show that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are derived for the matrix elements of different functions such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied. The transition probability between two eigenstates produced by a harmonic perturbation as a function of the operators [Formula: see text]±,0 is discussed. The average values of some observables in the coherent states |α > for the Morse potential are also calculated. PACS Nos.: 02.30+b, 03.65Fd, 42.50Ar, and 33.10Cs
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.
We obtain the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators. We next review a new method for obtaining the coherent states for arbitrary potentials, it being based on the classical motion of a particle. We apply this method to the Morse oscillator. After demonstrating that in the appropriate limit our results reduce to those for the harmonic oscillator, we obtain analytic insights into published numerical results on uncertainty products for Morse-oscillator wave packets.