Pseudoharmonic oscillator in quantum mechanics with a minimal length

Abstract

The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, (∆x) min = √ 5β. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration-rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules. * Electronic address: djamilbouaziz@univ-jijel.dz † Electronic address: abdelmalek-boukhellout@univ-jijel.dz

Generalized quantum similarity index: An application to pseudoharmonic oscillator with isospectral potentials in 3D

“…Let us consider the pseudoharmonic oscillator potential [ 1–16 ] where r is the internuclear distance between diatomic molecules. Therefore, the effective pair of isospectral potentials in one dimension is where …”

“…We have found some published papers where this potential was considered with and without θ-dependent potential. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Likewise, some oscillator potentials that are closely related to this potential have already been studied a few years ago. [17,18] Recently, bound-state solutions have been obtained for the Kratzer potential, [19,20] Morse, Pöschl-Teller potential, [21] Deng-Fan-Eckart potential, [22] and Aharanov-Bohm magnetic field, [18,19,23] and some of them have been investigated for information theoretic measures and the thermal properties of some molecules.…”

Kratzer’s molecular potential in quantum mechanics with a generalized uncertainty principle

“…For this purpose, following Ref. [68], we use the fact that the dimensionless parameter γ, in Eq. (31), is so large for most molecules (γ ≫ 1) [44], we may then expand E nℓ , given by Eq.…”

Deformed Heisenberg Algebra with a minimal length: Application to some molecular potentials

“…The minimal length seems to depend on the energy scale of the problem and might therefore characterize the size of the system under study [13,26]. The latter finding was behind the motivation of our recent investigations [1,2] on the GUP effects in diatomic molecules, because the spatial extension of these systems is relatively large, and the effect of the minimal length may clearly manifest.…”

“…Here, we review the main results obtained in [1,2]: We give the expression of the vibration-rotation energy spectrum of diatomic molecules in the presence of a minimal length by studying the deformed Schrödinger equation with the two potentials. In both cases, we apply the obtained formulas to compute the spectroscopic constants of diatomic molecules and investigate the effect of the GUP on these constants.…”