Energy Spectrum and the properties of the Schiöberg potential using the WKB approximation approach

Omugbe, E.; Osafile, O. E.; Okon, I. B.; Onyeaju, M. C.

doi:10.1080/00268976.2020.1818860

Cited by 13 publications

(9 citation statements)

References 43 publications

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“…The method of summation of rovibrational energies is more involved at high temperatures than the classical corrected method, which is basically a single one-dimensional integration (in case of diatomic molecule). In the summation method, even the highest rovibrational levels matter, so that there are many levels to be found with high accuracy, − but at lower temperatures the present method is not satisfactory so that these two approaches can be seen as complementary (the quantum based is recommended at low temperatures and the classical based is recommended at high temperatures).…”

Section: Methodsmentioning

confidence: 89%

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

Buchowiecki

2021

J. Phys. Chem. A

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The difficulties in calculation of high temperature heat capacities and discrepancies between available data are discussed in the case of the NH molecule. The source of those inaccuracies are the underlining potential energy curves. The relevant partition functions and heat capacities are calculated with the classical Wigner–Kirkwood corrected method. In addition to the ground electronic state, also four excited states are taken into account. Two potential energy curves and experimental energy levels of the ground state are considered.

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Section: Methodsmentioning

confidence: 89%

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

Buchowiecki

2021

J. Phys. Chem. A

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“…The approximate analytical solutions of one-dimensional radial Schrödinger equation with a multiple potential function have been studied using a suitable approximation scheme to the centrifugal term within the frame work of the parametric Nikiforov-Uvarov method [1]. The solutions to the wave equations in quantum mechanics and applied physics play a crucial role in understanding the importance of physical systems [2]. The two most important parts in studying Schrödinger equations are the total wave function and energy eigenvalues [3].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

Okon

Onate

Omugbe

et al. 2022

Advances in High Energy Physics

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In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

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“…Analytical equations (or statistical-mechanical models) for the prediction of thermal properties of gaseous substances are modeled not only in terms of the internal vibration of a molecule, the rotational and translational effects of the molecule are also taken into cognizance. Amongst the thermodynamic properties analyzed by statistical-mechanical models include Helmholtz free energy, mean thermal energy, entropy, enthalpy, Gibbs free energy, and heat capacities [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Isobaric molar heat capacity model for the improved Tietz potential

Eyube

Notani

Dlama

et al. 2022

Int J of Quantum Chemistry

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In this study, the improved Tietz potential was used to describe the internal vibration of diatomic molecules. By employing the expression for upper bound vibrational quantum number and canonical partition function of the system, equation for the prediction of constant pressure (isobaric) molar heat capacity of diatomic molecules was derived. The analytical model was used to predict the isobaric molar heat capacity of the ground state CO, BBr, HBr, HI, P2, KBr, Br2, PBr, SiO, and Cl2 molecules. The upper bound vibrational quantum number obtained for the molecules are 85, 100, 21, 21, 115, 301, 89, 157, 110, and 67. The calculated average absolute deviations are 2.3462%, 1.1342%, 2.3350%, 1.9078%, 0.7268%, 2.4041%, 1.7849%, 1.8989%, 2.5209%, and 2.1523% from experimental data. The results obtained are in good agreement with available literature data on gaseous molecules.

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Energy Spectrum and the properties of the Schiöberg potential using the WKB approximation approach

Cited by 13 publications

References 43 publications

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

Uncertainty of High Temperature Heat Capacities: The Case Study of the NH Radical

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

Isobaric molar heat capacity model for the improved Tietz potential

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