Path integral treatment of the deformed Schiöberg-type potential for some diatomic molecules

Abstract

The bound state solution of the Feynman propagator with the deformed generalized Schiöberg potential is determined using an approximation of the centrifugal term. The energy eigenvalue expression is computed using Duru–Kleinert space–time transformation for both positive and negative deformation parameters of diatomic molecules. Besides, the rotation–vibration energy eigenvalues are numerically calculated for some diatomic molecules and compared with those given in the literature. The obtained results are in agreement with those given by state-of-the-art approximate and numerical methods.

Improved multiparameter exponential‐type potential for diatomic molecules

“…[3] The emergence of the improved Tietz potential and its special cases has attracted great attention in the physical and chemical community due to a combination of simple forms and effective applications, including relativistic and nonrelativistic treatments of molecular vibrational energies and predictions of thermochemical quantities for some diatomics. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] Through the introduction of the dissociation energy and equilibrium bond length as direct parameter identifications, we have overcome the fault that the potential parameters appearing in the original MPETP given in Equation (1) lack explicit physical definitions. With the help of Equations (4) and (11), we obtain the following two expressions for calculations of the values of parameters k and q, [3]…”

“…Based on this manipulation, we can further represent the MPETP as the following improved form, This improved version tells us that the MPETP is entirely identical to the Tietz potential for diatomic molecules . The emergence of the improved Tietz potential and its special cases has attracted great attention in the physical and chemical community due to a combination of simple forms and effective applications, including relativistic and nonrelativistic treatments of molecular vibrational energies and predictions of thermochemical quantities for some diatomics . Through the introduction of the dissociation energy and equilibrium bond length as direct parameter identifications, we have overcome the fault that the potential parameters appearing in the original MPETP given in Equation lack explicit physical definitions.…”

Path integral discussion of the improved Tietz potential

“…In this case, the solutions of the Schrödinger equation are hypergeometric series 2 F 1 (a, b, c, z) with transcendental equations for energy levels. The same potential has been treated within the path integral approach by Amrouche et al [23] without incorporating the Dirichlet boundary conditions into the path integral. Likewise, their solutions for the cases −1 < q < 0 and q > 0 must be discarded as that of Mustafa.…”

“…Another interesting case, which despite appearances, presents some kinship with the potentials above is the new deformed Schiöberg-type potential introduced by Mustafa [22] to calculate the ro-vibrational energy levels of some diatomic molecules in the context of the supersymmetric quantum mechanics. This potential has also been discussed in an approach based on the Feynman path integral [23]. The potential function (2) contains three kinds of potentials namely the deformed modified Manning-Rosen potential [24] for q < 0, the deformed modified Rosen-Morse potential [25] when q > 0 and the Morse potential [26] at the limit q → 0.…”

“…Another interesting case, which despite appearances, presents some kinship with the potentials above is the new deformed Schiöberg-type potential introduced by Mustafa [22] to calculate the ro-vibrational energy levels of some diatomic molecules in the context of the supersymmetric quantum mechanics. This potential has also been discussed in an approach based on the Feynman path integral [23].…”