Morse Potential Energy Model Research Articles

Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.

The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler–MacLaurin method in one dimension

In this paper, we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function, the related thermodynamic functions are derived and studied in terms of the parameters of the model. Especially, we plotted the q-deformed vibrational partition function and vibrational specific heat for some diatomic molecule systems such as \(\text {H}_{2}\), HCl, LiH, and CO. The idea of a critical temperature \(T_{C}\) is introduced in relation to the specific heat.

Solutions of the Dirac equation with the Morse potential energy model in higher spatial dimensions

Analytical solutions of the Dirac equation with the Morse potential energy model in higher spatial dimensions have been explored. We present the bound-state energy equation and the corresponding upper and lower radial wave functions. We find that the behavior of the higher-dimensional relativistic vibrational energies remains similar to that of the three-dimensional molecular system for the \( {\rm X}^2\sum^+\) state of the CP molecule. This symmetry phenomenon will break at the critical point through which the system undergoes a phase transition from a stable to an unstable state.

Solutions of the Klein–Gordon equation with the Morse potential energy model in higher spatial dimensions

We solve the Klein–Gordon equation with the Morse potential energy model to obtain the relativistic bound state energy equation in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the Morse potential model. For a fixed vibrational quantum number and various rotational quantum numbers, the relativistic energies for the X1Σ+ state of the ScI molecule diverge as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Molecular spinless energies of the modified Rosen–Morse potential energy model in higher spatial dimensions

We solve the Klein–Gordon equation with the modified Rosen–Morse potential energy model in D spatial dimensions. The bound state energy equation has been obtained by using the supersymmetric WKB approximation approach. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the modified Rosen–Morse potential. For fixed vibrational and rotational quantum numbers, the relativistic energies for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical increase as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

D-dimensional energies for lithium dimer and silicon carbide radical

By using the supersymmetric shape invariance approach, we solve the Schrödinger equation with the modified Rosen–Morse potential energy model in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the modified Rosen–Morse potential energy model. The rotation-vibrational energies for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are observed to increase as D increases in the presence of a fixed vibrational quantum number and rotational quantum number. It is found that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system for these two molecular states.

D-dimensional energies for scandium monoiodide

We solve the Schrodinger equation with the Morse potential energy model in \(D\) spatial dimensions. The bound state rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For a fixed vibrational quantum number and various rotational quantum numbers, the energies for the \(\hbox {X}^{1}\Sigma ^{+}\) state of ScI molecule increase as \(D\) increases. We observe that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. The dimensional scaling method resembles a translation transformation from the higher dimensions to the actual three dimensions.

D-dimensional energies for cesium and sodium dimers

We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

Molecular energies of the improved Rosen−Morse potential energy model

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Molecular Spinless Energies of the Morse Potential Energy Model

We solve the Klein-Gordon equation with the Morse empirical potential energy model. The bound state energy equation has been obtained in terms of the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the <TEX>$X^1{\sum}^+$</TEX> state of ScI molecule have been computed by using the Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction

In this study, we obtain the approximate analytical solutions of the Dirac equation for an improved expression of the Rosen–Morse potential energy model including the Coulomb-like tensor under the condition of spin and pseudospin symmetry. The analytical approach of parametric generalization of the Nikiforov–Uvarov method has been applied to the problem and the problem is discussed in a quite detailed manner.

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $$\omega _e x_e $$ and $$\omega _e y_e $$ .

Equivalence of the deformed modified Rosen–Morse potential energy model and the Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed modified Rosen–Morse potential energy model. It is found that the deformed modified Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. In terms of the energy spectrum expression of the deformed modified Rosen–Morse potential model, we obtain exact closed-form expressions for diatomic anharmonicity constants ωexe and ωeye . The anharmonicity constants for the X1Σ+g state of the N2 molecule have been computed and compared with the observed data.