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Canadian Journal of Physics

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

Assia Amrouche, Ahmed Diaf, Mohammed Hachama

Published Oct 4, 2016• 18 citations
Publisher

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.

DOI
10.1139/cjp-2016-0397

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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.
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Abstract In this paper, we solve the Feynman Kernel for the q-deformed hyperbolic Scarf potential for any ℓ -states. We propose an accurate generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials which allows to transform our potential to a solvable shifted modified Pöschl-Teller one. Analytical expressions of the energy spectrum and the normalized ℓ -state eigenfunctions are derived from the Green function. We evaluate and compare our results to the literature. Furthermore, we apply our method in chemical physics to derive the spectrum of some diatomic molecules. We obtained good results compared to state-of-the-art competing analytical and numerical methods.
Abstract In this study, we investigated the approximate analytical bound state solutions of the Schrödinger equation, considering a linear combination of the deformed (Hulthén 1942 Ark. Mat. Astron. Fys. 28A 671) potential and the generalized (Kratzer 1920 Z. Phys. 3 289–307) potential. The analysis was performed within the path-integral formalism. Using an appropriate approximation to evaluate the centrifugal term, we derived the energy spectrum and normalized wave functions of the bound states from the poles of the Green’s function and its residues. To evaluate the accuracy and applicability of the derived expressions, we discuss several limiting cases of the potential and carry out numerical calculations of the energy levels, complemented by illustrative plots for selected diatomic molecules.
In this work, we present a rigorous and complete non-relativistic treatment of the problem of a diatomic molecule which moves under the Hua potential in a D-dimensional Euclidean space. The radial Green’s function associated with this potential is constructed within the framework of the Feynman path integral. Different cases of this potential which are distinguished by the values of the deformation parameter q are considered separately. For [Formula: see text] q < 1 and r ∈ ] r0, +∞[, we adopt an appropriate Pekeris-type approximation for the centrifugal potential term to obtain the approximate spectrum of bound states lD ≠ 0. Some numerical results of the energy levels of certain diatomic molecules are calculated by using the correct minimum value of the deformation parameter q given by [Formula: see text]. For q < 0 or [Formula: see text], the problem is solvable only in a three-dimensional space. In both cases, the energy quantization condition is a transcendental equation that can be solved numerically. In the limit [Formula: see text], the energy spectrum and the corresponding wave functions of the radial Morse potential are regained.
Abstract The approximate bound state solutions of Schrödinger equation with linear combination of a q-deformed Hulthén potential plus screened Kratzer potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briefly and it is found that obtained results are in good agreement with those obtained in the literature.
In this study, an approximate solution of the Schrödinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov–Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.