Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

Ikhdair, Sameer M.; Falaye, Babatunde J.

doi:10.1016/j.chemphys.2013.05.021

Cited by 73 publications

(41 citation statements)

References 76 publications

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“…[27], [29] and [31] and the conversion factors used are taken from NIST database [32]: 1cm −1 = 1.239841930eV,hc = 1973.29eVÅ and 1amu = 931.494061Mev/c 2 . In Table 2, we test the accuracy of the method utilized in this study by finding the energy spectra of H 2 and CO diatomic molecules.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Spectroscopic study of some diatomic molecules via the proper quantization rule

Falaye

Ikhdair²,

Hamzavi

2015

J Math Chem

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Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on theoretical analysis and computational calculations. In this research, we apply the proper quantization rule in spectroscopic study of some diatomic molecules by solving the Schrödinger equation with two solvable quantum molecular systems-Tietz-Wei and shifted DengFan potential models for their approximate nonrelativistic energy states via an appropriate approximation to the centrifugal term. We show that the energy levels can be determined from its ground state energy. The beauty and simplicity of the method applied in this study is that, it can be applied to any exactly as well as approximately solvable models. The validity and accuracy of the method is tested with previous techniques via numerical computation for H 2 and CO diatomic molecules. The result also include energy spectrum of 5 different electronic states of NO and 2 different electronic state of ICl.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Spectroscopic study of some diatomic molecules via the proper quantization rule

Falaye

Ikhdair²,

Hamzavi

2015

J Math Chem

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“…To verify the energetic behavior of

H Cl

molecules, we have compared some of the most important thermodynamic functions in analogy with other authors . We calculated the Morse potential and the EP parameters.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Valencia-Ortega

Arias-Hernandez

2018

Int J of Quantum Chemistry

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Due to one of the most representative contributions to the energy in diatomic molecules being the vibrational, we consider the generalized Morse potential (GMP) as a typical interaction for one‐dimensional microscopic systems, which describes local anharmonic effects. From the Eckart potential (EP) model, it is possible to find a connection with the GMP model, as well as obtaining the analytical expression for the energy spectrum because it is based on SOtrue(2,1true) algebras. This gives the macroscopic properties such as vibrational mean energy U, specific heat C, Helmholtz free energy F, and entropy S for a heteronuclear diatomic system, as well as with the exact partition function and its approximation for the high temperature region. Finally, a comparison is made between the graphs of some thermodynamic functions obtained with the GMP and the Morse potential (MP) for H Cl molecules.

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“…The imaginary error function is an entire function defined by Erfi.x/ D iErf .ix/, and this function is implemented in mathematica as ErfiOEx, where erf denotes the error function is a special function of sigmoid shape, which occurs in probability, statistics, and partial differential equations. In mathematics, the error function can be denoted as [41,42] Erf .x/ D 2 ıp R x 0 e t 2 dt. Other thermodynamic properties of the system can be easily obtained from partition function.…”

Section: First Potentialmentioning

confidence: 99%

“…In Eq. (30), the Dowson function or Dowson integral can be denoted as [41,42] F.x/ D e x 2 R x 0 e y 2 dy D p ı 2 e x 2 erfi.x/. Thus, the Dowson's integral is implemented in mathematica as DowsonFOEx.…”

Section: First Potentialmentioning

confidence: 99%

Non‐relativistic Eigen spectra with q‐deformed physical potentials by using the SUSY approach

Eshghi

Mehraban

Ghafoori

2016

Math Methods in App Sciences

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The Schrödinger equation is solved for some of the q‐deformed physical potentials within the framework of supersymmetric approach and supersymmetric Wentzel–Kramers–Brillouin approximation method. The energy levels are obtained with the corresponding normalized wave functions in terms of hypergeometric functions. The energy equations for some special cases of these potentials are discussed, and some of the thermodynamic quantities of the canonical system and the optical quantities of the two‐level system are calculated for one of the potentials. Some of the numerical results are shown, too. Copyright © 2016 John Wiley & Sons, Ltd.

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Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

Cited by 73 publications

References 76 publications

Spectroscopic study of some diatomic molecules via the proper quantization rule

Spectroscopic study of some diatomic molecules via the proper quantization rule

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Non‐relativistic Eigen spectra with q‐deformed physical potentials by using the SUSY approach

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