Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

Abdelmonem, M. S.; Abdel-Hady, Afaf; Nasser, Ibraheem

doi:10.1002/qua.24968

Cited by 3 publications

(1 citation statement)

References 45 publications

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“…One of the most important tasks discussed in physics is to obtain the exact analytical solutions, which describe the bound and scattering states, of radial Schrödinger equation with arbitrary angular quantum numbers (l = 0 and l = 0) for various potentials. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] For the s-wave states (the case of l = 0), the analytical solutions for the bound states can be achieved directly. On the other hand, for the l-wave states (the case of l = 0), it is necessary to use a convenient approximation to the centrifugal term (l(l + 1)/r 2 ) such as the Pekeris approximation [17] and the approximation scheme proposed by Greene and Aldrich.…”

Section: Introductionmentioning

confidence: 99%

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

Taş

Havare

2017

Chinese Phys. B

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In this study, we present the analytical solutions of bound states for the Schrödinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l (states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.

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Section: Introductionmentioning

confidence: 99%

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

Taş

Havare

2017

Chinese Phys. B

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Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential

Abamba,

Kolebaje,

Vincent

et al. 2024

Phys. Rev. E

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For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, H2, N2, Cl2, I2, O2, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation. Published by the American Physical Society 2024

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A formula of Tietz potential parameters and applying for scandium iodine, nitrogen iodine, rubidium hydride, nitrogen, and carbon monoxide molecules

Al‐Raeei

2023

Can. J. Phys.

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Tietz potential has several applications in the study of diatomic molecules in the discussing of vibrational states, especially, in the quantum mechanics studies of the oscillations. Tietz potential has multiple forms, one of the Tietz potential forms has four parameters of the spectroscopic fitting. The spectroscopic fitting parameters of the Tietz potential are the Tietz potential equilibrium bond length, the Tietz potential depth, the width of the potential, and the parameter which controls the values as ratio of the depth of the well. This work focuses on finding a formula between the four parameters of the spectroscopic fitting employing some of principles of the statistical mechanics. Based on the derived formula, we discuss the relationship of the equilibrium bond length of Tietz potential interaction as function to the absolute temperature. Based on this discussion, the equilibrium bond length of Tietz potential interaction varies slowly with absolute temperature. Besides, equilibrium bond length of Tietz potential varies linearly with the radius of the particles of the system. Also, the equilibrium bond length of Tietz potential varies with the Tietz potential depth, the width parameter of Tietz potential, and the fourth parameter of the Tietz potential. The formula of the Tietz interaction is applied for five different dimers or molecules. The five considered molecules are Nitrogen dimer, scandium iodine dimer, nitrogen iodine dimer, rubidium hydride dimer, and carbon monoxide molecule. Generally, it is found that the equilibrium bond length of Tietz potential interaction values vary from 1 Angstrom to 5 Angstrom for different absolute temperatures intervals. Besides, it is found that the scandium iodine dimer has the largest value of the equilibrium bond length of Tietz potential interaction, while carbon monoxide dimer has the lowest value of the equilibrium bond length of Tietz potential interaction.

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Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

Cited by 3 publications

References 45 publications

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential

A formula of Tietz potential parameters and applying for scandium iodine, nitrogen iodine, rubidium hydride, nitrogen, and carbon monoxide molecules

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