.
Within the framework of non-relativistic quantum mechanics via the Nikiforov-Uvarov (NU) method, we obtained the energy eigenvalues and the corresponding normalized eigenfunctions of a newly ...proposed screened Kratzer potential for lithium hydride (LiH) and hydrogen chloride (HCl) diatomic molecules. With the help of the Hellman-Feynman theorem, the expressions for the expectation values of the square of inverse of position,
r
-
2
, inverse of position,
r
-
1
, kinetic energy,
T
, and square of momentum,
p
2
, and their respective numerical values for the selected diatomic molecules are presented. The vibrational partition function and other thermodynamic functions are also obtained in closed form for the diatomic molecules, using the energy eigenvalues. The results obtained clearly agree with the previously obtained results in the literature.
The Deng–Fan–Eckart potential is as good as the Morse potential in studying atomic interaction in diatomic molecules. By using the improved Pekeris-type approximation, to deal with the centrifugal ...term, we obtain the bound-state solutions of the radial Schrödinger equation with this adopted molecular model via the Factorization Method. With the energy equation obtained, the thermodynamic properties of some selected diatomic molecules (H
2
, CO, ScN and ScF) were obtained using Poisson summation method. The unnormalized wave function is also derived. The energy spectrum for a set of diatomic molecules for different values of the vibrational
n
and rotational
ℓ
are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the Deng–Fan potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods.
We have solved the Schrodinger equation with the modified Kratzer plus screened Coulomb potential using the modified factorization method. We have also employed both the Greene–Aldrich approximation ...scheme and a suitable transformation scheme to obtain the energy eigenvalues equation and its corresponding energy eigenfunctions for CO, NO, and N
2
diatomic molecules. Numerical results of the energy eigenvalues for the selected diatomic molecules have been computed and discussed. The effects of the combined potential parameters on the energy eigenvalues have been evaluated. We have used the energy eigenvalues of the modified Kratzer plus screened Coulomb potential to obtain the vibrational partition functions and other thermodynamic functions for the selected diatomic molecules. Our results are relevant in other areas of theoretical physics and chemistry, and they agree perfectly with the results obtained in the literature.
A new method for solving second order differential equation called “Nikiforov–Uvarov-Functional-Analysis (NUFA) method is generalized. This method is employed to obtain the eigensolutions of the ...radial Schrodinger equation with selected exponential-type potential models. The NUFA method is seen to be easy and efficient, eliminating the rigorous mathematical manipulations encountered in other methods. Our results agree perfectly with the ones in different literatures.
In this work, the thermodynamic properties of pseudo-harmonic potential in the presence of external magnetic and Aharanov-Bohm fields are investigated. The effective Boltzmann factor in the ...superstatistics formalism was used to obtain the thermodynamic properties such as Helmholtz free energy, Internal energy, entropy and specific heat capacity of the system. In addition, the thermal properties of some selected diatomic molecules of N2,Cl2,I2 and CH using their experimental spectroscopic parameters and the effect of varying the deformation parameter of q=0,0.3,0.7 were duly examined.
Statistical physics; Thermodynamics; Quantum mechanics; Superstatistics, Pseudo-harmonic potential, Schrödinger equation, Partition function.
In this research work, the Hellmann potential is studied in the presence of external magnetic and AB flux fields within the framework of Schrodinger equation using the Nikiforov–Uvarov functional ...analysis method. The energy equation and wave function of the system are obtained in closed form. The effect of the fields on the energy spectra of the system is examined in detail. It is found that the AB field performs better than the magnetic field in its ability to remove degeneracy. Furthermore, the magnetization and magnetic susceptibility of the system were discussed at zero and finite temperatures. We evaluate the partition function and use it to evaluate other thermodynamic properties of the system such as magnetic susceptibility,
χ
m
B
→
,
Φ
AB
,
β
, Helmholtz free energy
F
B
→
,
Φ
AB
,
β
, entropy
S
B
→
,
Φ
AB
,
β
, internal energy
U
B
→
,
Φ
AB
,
β
and specific heat
C
v
B
→
,
Φ
AB
,
β
. A comparative analysis of the magnetic susceptibility of the system at zero and finite temperatures shows a similarity in the behavior of the system. A straightforward extension of our results to three dimensions shows that the present result is consistent with what is obtained in the literature.
The Dirac equation is solved approximately for the Woods-Saxon potential and a tensor potential with the arbitrary spin-orbit coupling quantum number
under pseudospin and spin symmetry. The energy ...eigenvalues and the Dirac spinors are obtained in terms of hypergeometric functions. The energy eigenvalues are calculated numerically.
Abstract
We solve the D- dimensional Klein–Gordon equation with a newly proposed generalized hyperbolic potential model, under the condition of equal scalar and vector potentials. The relativistic ...bound state energy equation has been obtained via the functional analysis method. We obtained the relativistic and non-relativistic ro-vibrational energy spectra for different diatomic molecules. The numerical results for these diatomic molecules tend to portray inter-dimensional degeneracy symmetry. Variations of the energy eigenvalues obtained with the potential parameters have been demonstrated graphically. Our studies will find relevant applications in the areas of chemical physics and high-energy physics.
PDF
