Narrow Results

The thermal properties of three diatomic molecules such as hydrogen (H₂), carbon monoxide (CO) and iodine (I₂) are theoretically predicted. To this end, two different potential models are considered, Morse potential and improved deformed exponential-type potential (IDEP). The Schrödinger equation is analytically solved to obtain energy levels. For the Morse and IDEP potential models, the Laplace transformation and the Greene–Aldrich approximation and appropriate coordinate transformation are employed, respectively. In the former potential model, we have obtained energy eigenvalues by considering position-dependent effective mass. Using the energy levels of two models, the partition function is first determined. Second, thermal functions of the molecules such as heat capacity, enthalpy and entropy are obtained and compared with the available results. The calculated enthalpy using the two models for CO and I₂ molecules is in excellent agreement in comparison with the available data in a wide temperature range. But, the obtained enthalpy of H₂ molecule using the Morse potential at high temperatures does not agree excellently with the experimental data. The entropy of H₂, CO and I₂ using the two models is tin good agreement in comparison with the available data in a wide temperature range whereas the entropy of H₂ at low temperatures does not agree excellently with the experimental data. Our theoretical results using the two potential models do not show a suitable prediction about the heat capacity at a constant pressure of H₂, CO and I₂ molecules, But the IDEP shows more agreement compared to the Morse potential.

By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

The position and momentum space information entropies for the Morse potential are numerically obtained for different strengths of the potential. It is found to satisfy the bound obtained by Beckner, Bialynicki-Birula, and Mycielski. Interesting features of the entropy densities are graphically demonstrated.

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of ¹⁹²Pt, ¹⁹⁴Pt and ¹⁹⁶Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

In this paper, we investigate theoretically the effects of electric field on the linear and nonlinear optical properties of Morse quantum wells considering a two-level system. The effective mass approximation and the envelope function approach are used to calculate the energy levels and wave functions. The analytical expressions of the optical properties are obtained by using the compact density-matrix approach. The linear and third-order nonlinear optical absorption coefficients and the refractive index changes are investigated as a function of the incident photon energy for several configurations of the structural parameter and the applied electric field. Numerical results, presented for a typical GaAs/AlGaAs quantum well, reveal that the electric field has a significant effect on the optical characteristics of these structures and intersubband transitions can be modified by tuning the structural range parameter of the potential.

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

For the needs of non-perturbative quantum theory, an upgraded concept of solvability is proposed. In a broader methodical context, the innovation involves Schrödinger equations which are piecewise analytic and piecewise solvable in terms of special (in our illustrative example, Whittaker) functions. In a practical implementation of our symbolic-manipulation-based approach, we work with a non-analyticity in the origin. A persuasive advantage is then found in the both-sidedness of our iterative localization of the energies.

We have obtained the creation and annihilation operators directly from the eigenfunction for the general deformed morse potential in one-dimensional Klein–Gordon equation with equally mixed vector and scalar potentials and also in the Schrödinger equation, we show that these operators satisfy the commutation relation of the SU(1, 1) group. Then we have expressed the Hamiltonian in terms of the su(1, 1) algebra.