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Context: In this paper, the approximate analytical energy equations for the deformed hyperbolic potential have been obtained for arbitrary parameters of the potential. The potential function was transformed to a molecular potential by subjecting it to the Varshni conditions which allows for the determination of the energy levels of diatomic molecules. The molecular vibrational energy spectra for L i 2 (G 1 Π g) , N 2 (X 1 ∑ g +) , R b H (X 1 ∑ +) , N I (b 1 ∑ +) , and B r F (X 1 ∑ +) diatomic molecules were obtained and found to match with the results obtained with another analytical approach, potential functions, and experimental data. The noticeable slight differences in the approximate energy spectra obtained in this work and existing literature may be ascribed to the analytical method, computational approach, and the accuracy of the molecular potential functions. The obtained energy equations were used to determine the energy of a particle for arbitrary parameters of the potential function. The obtained energy is bounded and increases with the increase in the quantum numbers. The results conformed to the ones obtained via the path integral approach and numerical solutions obtained via the MATHEMATICA program. Method: The energy spectra equations were obtained via the Nikiforov-Uvarov approach and semi-classical WKB approximation. The Pekeris approximation has been applied to resolve the difficulty in solving the complete energy spectrum of the non-relativistic wave equation for the potential function. The numerical data of the energy spectra was obtained using the MATHEMATICA program. [ABSTRACT FROM AUTHOR]

The Fisher information-theoretic measurement and the oscillator strength are studied with a mixed hyperbolic Pöschl–Teller potential (MHPTP). Using the total energy eigenvalue equation obtained via the super-symmetric WKB approach as well as the total wave function. We obtained the oscillator strength for the atomic transitions 1 s - 2 p and 1 s - 3 p , where the strength length decreased with increasing potential screening parameters. Also, the Fisher information entropies for both position and momentum spaces are obtained numerically. We studied the correlation between potential parameters and the energy spectra graphically. Our results for the information-theoretic measures obey the Fisher's uncertainty product and the Cramer–Rao inequality in position space. The analytical result for the N -dimensional energy eigenvalue obtained by the super-symmetric WKB approach is the same as the result obtained by a different analytic approach in the existing literature. The oscillator strength conforms to the ones reported in existing literature using different potential energy functions. [ABSTRACT FROM AUTHOR]

In this paper, we have obtained the analytical and numerical mass spectra of the charmonium and bottomonium mesons using the non-relativistic Schrödinger equation under a spin–spin, spin–orbit and tensor coupled Cornell potential energy. We adopted the Wentzel–Kramers–Brilluoin approximation method to obtain the energy bound equation in closed form. We obtained the potential free parameters by fitting the mass spectra equation to the experimental data of the Particle Data Group. The hyperfine mass splitting of the mesons are obtained for different singlet ( s = 0) and triplet ( s = 1) quantum states ( n 2 s + 1 l j) . Also, the hyperfine multiplet splitting for l > 0 and total angular momentum quantum number j = l , j = l ± 1 were obtained. The results revealed that the charmonium masses ψ (n 3 S 1) and η c (n 1 S 0) ( n = 2 , 3 , 4 , 5 , 6) and bottomonium masses ( η b (n 1 S 0)) and Υ (n 3 S 1) ( n = 2 , 3 , 4 , 6) for the s-wave quantum states are in good agreement with the results obtained by other methods in the existing literature and available experimental data. For l > 0 , the charmonia masses χ c j (n 3 P j) ψ 1 1 3 D 1 and ψ 2 2 3 D 1 agreed with the works obtained using other potential models and observed data. In comparison to experimental data, the total absolute deviation error of 3.21% and 1.06% was obtained for the respective charmonium and bottomonium masses. The proposed potential model provides a satisfying account for the mass spectra of the heavy mesons and may be extended to study other spectroscopic parameters. [ABSTRACT FROM AUTHOR]

We investigated the effects of external magnetic and Aharonov–Bohm flux fields on the thermodynamic properties, Fisher, Shannon and Rényi information-theoretic measures using the non-relativistic Schrödinger equation with a Varshni-type potential. We adopted the parametric Nikiforov–Uvarov approach to obtain the analytical bound states in closed form. The thermodynamic functions such as the free energy, specific heat capacity, vibrational entropy and mean energy were analyzed. Also, the results for the 2D Fisher's information-theoretic measure obey the inequality I ρ I γ ≥ 16 . The Rényi entropies sum applied to lithium hydride (LiH) diatomic molecule obeys the inequality R 2 ρ + R 2 / 3 γ ≥ 4.19926 for 2D system. Also, the global Shannon entropies sum inequality for the LiH molecule is verified. The applications of the external fields were found to strongly influence the splitting of the energy overlaps, the thermodynamic functions and the information-theoretic measures. The results may aid the understanding of the dynamics of quantum particles and molecules in external fields. [ABSTRACT FROM AUTHOR]

We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving in a quantum mechanical solvable potential under the influence of the external magnetic and Aharonov–Bohm flux fields. We utilized the supersymmetric WKB approach to obtain both the energy levels and normalized wave function in closed form. The proposed potential reduces to the screened Kratzer, Kratzer, Yukawa and Coulomb potential functions as special cases and admits the corresponding energy eigenvalues in both relativistic and non-relativistic regimes. When the external magnetic and Aharonov–Bohm flux fields were turned off, the relativistic, non-relativistic energies and ground state probability density overlap for the magnetic quantum numbers ( m = - 1 , 1 ). The presence of the fields removes the degeneracy and shifts the energy levels of the Klein–Gordon particle. However, we found that the magnetic field strength has no effects on the maximum non-relativistic energy. Generally, the results are consistent with the works in existing literature where the authors utilized different forms of potential energy functions. [ABSTRACT FROM AUTHOR]

The analytical solutions of the Dirac equation are presented in this paper in the presence of external fields using the formula method with the pseudoharmonic potential. The exact spin symmetry and pseudospin symmetry case are examined. Using a mapping to the non-relativistic limit for the exact spin symmetry limit, the non-relativistic energies are obtained both in the presence of the external field and in the absence of the field (in 3D). As an application, the non-relativistic energy eigenvalues of the N2, CH, CO and NO molecules under the influence of the external fields is presented. Furthermore, the ro-vibrational energies of the selected molecules are obtained in 3D. The results of the study are found to be consistent with the literature with the small variation arising from methodology and possibly due to difference in the conversion factors used for obtaining the energy of the molecules. [ABSTRACT FROM AUTHOR]

The study presents approximate solutions of Schrodinger equation with the Inversely quadratic Hellmann-Kratzer (IQHK) potential. The energy eigenvalues and corresponding wavefunctions are obtained analytically using the Nikiforov-Uvarov (NU) method. The expectation values of inverse position r−1, square of inverse position, r−2, kinetic energy, T, potential energy, V, and square of momentum, p2, and their respective numerical values are evaluated via the Hellmann–Feynman theorem. Special cases of IQHK potential are also reported. [ABSTRACT FROM AUTHOR]

The approximate solutions of Schrödinger equation for the Hua plus modified Eckart potential are obtained using the parametric Nikiforov–Uvarov method. By the use of a suitable approximation to deal with the centrifugal term, we obtained analytical expressions of the eigenvalues and corresponding wave functions. Numerical results of the energy eigenvalue are presented. Also, special cases of this potential are discussed and their energy eigenvalues evaluated. [ABSTRACT FROM AUTHOR]