Eigensolution techniques, expectation values and Fisher information of Wei potential function

Onate, C. A.; Onyeaju, M. C.; Bankole, Deborah Temitope; Ikot, Akpan N.

doi:10.1007/s00894-020-04573-4

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…As a result of the diverse applications of the theoretic information, it becomes necessary to implement the theoretic information with well-known molecular potentials that the eigensolutions agree with the Rydberg-Klein-Rees (RKR) and spectroscopic experimental data [20][21][22][23][24][25][26][27][28][29][30]. In a related development, the theoretic quantities of some molecular potential have also been studied [3,[31][32][33][34][35]. For instance, the eigensolutions, Shannon Entropy, and Fisher information under the Eckart-Manning-Rosen potential model have been investigated [33].…”

Section: Introductionmentioning

confidence: 99%

“…[34], the effect of dissociation energy on the Shannon and Renyi entropies was investigated also using the generalized Morse potential model. The eigensolutions techniques, expectation values, and Fisher information of the Wei potential function for the non-relativistic wave equation have also been obtained [35]. On the other hand, the concept of statistical quantum mechanics over the years has assisted in describing the dynamics of particles at the microscopic (ensemble of states) levels.…”

Section: Introductionmentioning

confidence: 99%

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Information theory and thermodynamic properties of diatomic molecules using molecular potential

Onyeaju,

Omugbe,

Onate

et al. 2023

J Mol Model

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In this paper, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for 〈𝑟〉, 〈𝑟 2 〉, and 〈𝑝 2 〉 were obtained to verify Heisenberg's uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H 2 , N 2, O 2, and HF). The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Information theory and thermodynamic properties of diatomic molecules using molecular potential

Onyeaju,

Omugbe,

Onate

et al. 2023

J Mol Model

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“…Using the Hellman-Feynman theory, expectation values of time and momentum were used to determine the Fisher information (for time and momentum) and variance (for time and momentum). Also, Under the influence of an improved expression for the Wei potential energy function, Onate et al, [50] obtained an approximate solution of the one-dimensional Klein-Gordon equation. By using specific mappings, it was possible to derive the solution of the SE from that of the Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to The Schrödinger Equation with Collective Potential Models: Application to Quantum Information Theory

Inyang¹,

Ayedun²,

Ibanga³

et al. 2022

East Eur. J. Phys.

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In this study, the energy equation and normalized wave function were obtained by solving the Schrödinger equation analytically utilizing the Eckart-Hellmann potential and the Nikiforov-Uvarov method. Fisher information and Shannon entropy were investigated. Our results showed higher-order characteristic behavior for position and momentum space. Our numerical results showed an increase in the accuracy of the location of the predicted particles occurring in the position space. Also, our results show that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality and Fisher information was also satisfied for the different eigenstates. This study's findings have applications in quantum chemistry, atomic and molecular physics, and quantum physics.

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Pure-vibrational spectrum of diatomic molecules using an improved Pöschl–Teller potential

Onate

Okon²,

Vincent³

et al. 2023

Chemical Physics

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Eigensolution techniques, expectation values and Fisher information of Wei potential function

Cited by 6 publications

References 24 publications

Information theory and thermodynamic properties of diatomic molecules using molecular potential

Information theory and thermodynamic properties of diatomic molecules using molecular potential

Analytical Solutions to The Schrödinger Equation with Collective Potential Models: Application to Quantum Information Theory

Pure-vibrational spectrum of diatomic molecules using an improved Pöschl–Teller potential

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