In this paper, we solved the Schrodinger equation with Hellmann-modified Kratzer potential using Nikiforov-Uvarov-Functional Analysis (NUFA) method. The obtained energy is used to study the numerical results of the ro-vibrational energy spectra for some selected diatomic molecules and their thermodynamic properties. In addition, we also investigated the Fisher information for three diatomic molecules and they all satisfied the Stam-Cramer-Rao inequalities uncertainty relations. Special cases of the potential are discussed and we compute the numerical eigenvalue of the modified Kratzer, Kratzer-Feus and Hellmann potentials for comparison with other analytical methods. The results of the present study agree with the results obtained with other known methods.
In this work, we proposed a screened modified Krazer potential and use the newly proposed by Analysis (NUFA) method to obtain the energy spectrum and the corresponding wave function. With the obtained energy spectrum, we studied the numerical results for some selected diatomic molecules and our results are in good agreement with other analytical method. We also evaluated the vibrational partition function for , and diatomic molecules via the Euler–Maclaurin approach and other thermodynamic functions such as free energy, entropy, mean energy and specific heat Capacity. The expectations values of and are also calculated numerically for different diatomic molecules using the normalized wave function for the two low lying states corresponding to the ground and first excited states. Our numerical results for the selected diatomic molecules validate the Heisenberg uncertainty relation, .
The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. Firstly, the Schrodinger equation is solved exactly using the Nikiforov-Uvarov-Functional Analysis (NUFA) method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low lying states corresponding to the ground and first excited state. The positions and momentum Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki-Birula and Mycielski (BBM) and the Stam-Cramer-Rao inequalities for the Shannon entropy and Fisher Information entropies respectively were tested and was found to be satisfied for all cases considered
In this paper, the Shannon entropy and Fisher information are studied for the screened Kratzer potential model (SKP). We calculated the position and momentum entropies for the screened Kratzer potential for its ground states as well as the first excited state. Our result shows that the sum of the position and momentum entropies satisfies the lower bound Berkner, Bialynicki–Birula and Mycieslki (BBM) inequality. Also, our results showed that decreasing Shannon entropy in the position space was complemented with an increasing Shannon entropy in the momentum space. Similarly, we evaluated for Fisher information and show that the Stam, Cramer-Rao inequalities are satisfied. The squeezing phenomena were also observed for certain values of the screening parameter α.