Generalized and Gaussian coherent states for the Morse potential

Abstract

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, 1H35Cl.

Squeezed coherent states and the one-dimensional Morse quantum system

“…The CS are not exactly eigenstates of the annihilation operator A − but we have shown [20] that, in practice, the last terms on the right-hand side of the sum in (1) do not contribute significantly. In some approaches (see, for example, [24]), these states are called pseudo-CS.…”

“…As mentioned in the introduction, the quantity k(n) in (2) is not unique and we consider two natural choices [20]. The first choice, the 'oscillator-like', corresponds to k(n) = n. The ladder operators satisfy an h(2) algebra.…”

“…Now, for a quantum system which admits a finite discrete spectrum like the one which involves the Morse potential, various constructions of CS have been adapted [16][17][18][19]. In a recent paper [20], we have used ladder operators [21,22] to construct different types of CS of the Morse potential and have compared them with the so-called Gaussian CS [23].…”

Phase space picture of Morse-like coherent states based upon the Wigner function

“…[30]. For the same system, it is also important to mention the generalized coherent statesà la Klauder [31] introduced by Angelova and Hussin [32], which turned out to be, as well, approximate coherent states inside the confining region of the potential. Using the Gazeau-Klauder formalism [7], in Ref.…”

Trajectories of generalized quantum states for systems with finite discrete spectrum and classical analogs

“…Our previous works [13,14] show that, for the Morse potential, such constructions have the advantage of good localization and minimum uncertainty for a range of values of the parameters z and γ. It also follows similar constructions for systems with an infinite discrete energy spectrum [15].…”