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Journal of Physics Conference Series

Arbitrary ℓ-state solutions of the Feynman propagator with the Deng-Fan molecular potential

Ahmed Diaf

Published Jan 21, 2015• 5 citations
Publisher

Abstract

The bound state solutions of the Feynman propagator with the rotating Deng- Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods.

DOI
10.1088/1742-6596/574/1/012022

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The bound state solutions of the Feynman propagator with the rotating Deng- Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods.
In this paper, we present analytic solutions of the Feynman propagator with the Rosen–Morse potential. To this end, an approximation of the centrifugal potential for any l state is used and nonlinear space–time transformations in the radial path integral are applied. A transformation formula that relates the original path integral to the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrödinger formalism. The Eckart potential is also treated as a special case.
The bound state solutions of the Schrödinger equation with the rotating Deng-Fan molecular potential are presented approximately. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived. To show the accuracy of our results, the eigenvalues calculated numerically for arbitrary quantum numbers n and l with two different values of the parameter r e are in good agreement with those obtained by the MATHEMATICA package for short potential range.
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 This paper presents an analytical path-integral treatment of the ℓ -states of an exponential-type potential. We propose a generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials. To obtain solutions of the radial Feynman Kernel for arbitrary angular number, we perform a nontrivial change of variable accompanied by a local time rescaling. Using Euler angles and the isomorphism between S 3 and SU (2), we convert the radial path integral into a maniable one. Analytical expressions of the energy spectrum and the normalized ℓ -state eigenfunctions are derived from the Green function. Several potentials are obtained as special cases of the general exponential-type potential. Thus, their eigenvalues and eigenfunctions are deduced straightforwardly. Numerical results show that our technique improves the state-of-the-art.
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.