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arXiv:1806.00717 · Journal of Physics A Mathematical and Theoretical

Morse-like squeezed coherent states and some of their properties

O de los Santos-Sánchez, J. Récamier

Published Aug 23, 2013• 7 citations
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Abstract

Using the f-deformed oscillator formalism, we introduce a class of squeezed coherent states for a Morse potential system (Morse-like squeezed coherent states) defined as approximate eigenstates of a linear combination of f-deformed ladder operators. For the states thus constructed, we analyze their statistical properties, their uncertainty relations, their Wigner function and their temporal evolution on phase space.

DOI
10.1088/1751-8113/46/37/375303

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Using the f-deformed oscillator formalism, we introduce a class of squeezed coherent states for a Morse potential system (Morse-like squeezed coherent states) defined as approximate eigenstates of a linear combination of f-deformed ladder operators. For the states thus constructed, we analyze their statistical properties, their uncertainty relations, their Wigner function and their temporal evolution on phase space.
The Morse potential quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.
The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
Abstract. The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule. 1.
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.