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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.

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.

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.

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.

We present an oscillator model of relativistic spin-0 charges moving in quantum states with minimal electromagnetic field coupling. Rather than using a perturbative approach, we implemented anharmonicity directly under the integer-dependent levels. In this way, the rest mass energy is kept at 280MeV. Within the extended Pekeris approximation, we have also improved the deep approximation to the third and fourth orders near equilibrium at 7.5fm with a width range of $0.43{\mathrm{\text{fm}}}^{-1}$. By taking into account the Morse potential energy, the improved approximation provides a model for the relativistic quantum states of the spatially independent rest mass without an external magnetic field. We considered an extra-energy addition that results in shifted Morse potentials in the depth range of 80–100MeV, yielding positive and negative values for particles and antiparticles, respectively. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels, where we have found about 200MeV for particles and nearly $-$10MeV for antiparticles. In addition to the negative energy states, the wave functions ($n=0$, $\ell =0$) and ($n=1$, $\ell =1$), which correspond to the energy levels, have been followed by the typical probability form, which shows charge distribution.

In this paper, we systematically investigate the cluster decay half-lives of heavy nuclei using the Wentzel–Kramers–Brillouin method and Bohr–Sommerfeld quantization condition for the Morse molecular potential. We determine the optimal nuclear potential parameters that best fit the experimental data of known cluster decay half-lives. Subsequently, we theoretically calculate the cluster decay half-lives for the heavy nuclei lacking experimental decay half-lives. Our findings reveal that the Morse model is highly effective in explaining the decay half-lives of the heavy nuclei, particularly when utilizing two degrees of freedom. This approach produces results that match the accuracy of empirical models found in the existing literature. Theoretical determinations of cluster decay half-lives with optimally derived model parameters are expected to guide future experimental studies.

We present in this letter a realistic construction of the coherent states for the Morse potential using the Klauder–Perelomov approach. We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

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.

The propagation of an initially Gaussian wave packet of width ${\mathrm{\Delta }}_0$ in Gross–Pitaevskii equation is extensively studied both for attractive and repulsive interactions. It is predicted analytically and verified numerically that for a free particle with attractive interaction, the dynamics of the width is governed by an effective potential which is sensitive to initial conditions. If ${\mathrm{\Delta }}_0$ is equal to a corresponding critical width ${\mathrm{\Delta }}_c$, then the packet will propagate in time with very little change in shape. These are in essence like coherent states. Whereas, if $\mathrm{\Delta }\ne {\mathrm{\Delta }}_c$, depending on the nature of the effective potential for chosen ${\mathrm{\Delta }}_0$ and the interaction strength $(|g|)$, the width of the packet in course of time, either oscillates with bounded width or will spread like a free particle. For a simple harmonic oscillator (SHO) also, we find that for ${\mathrm{\Delta }}_0$ smaller than a critical value, there always exists a coupling strength for which the packet simply oscillates about the mean position without changing its shape, once again providing a resemblance to a coherent state. We also consider the Morse potential, which interpolates between the free particle and the oscillator. For large attractive interactions, the two limiting dynamics (free and simple harmonic) are indeed observed but in the intermediate form of the potential where the nonlinear terms dominate in the dynamics, an initial Gaussian wave packet does not retain its shape. For repulsive interaction, the Gaussian packet always changes shape no matter what the system parameters are.

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.

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.

The interatomic interactions in a diatomic molecule can be fairly modeled by the Morse potential. Short range interactions of the molecule with the neighboring environment can be analyzed by modifying this potential by delta functions. Energy spectra and radial matrix elements have been calculated using an accurate nine-point finite-difference method for such an interacting homonuclear diatomic molecule. The effect of the strength and position of a single delta function interaction on the alignment of this molecule has been studied. The dependence of alignment on the strength of applied field has also been analyzed.

We show that a Morse-type potential simulates an analytic solution for the highly nonlinear global monopole field equation in three and higher-dimensional flat spacetimes. Owing to the fact that in the flat space limit the similar equation remains intact, we wish to borrow the curved space terminology of global monopole also in flat spacetime. This may provide a compelling example that can be used effectively in different nonlinear theories such as flat space ${\varphi }^4,$ as well as in curved spacetimes.