Analytical solution of the Feynman Kernel for general exponential-type potentials

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 S3 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.

Improved multiparameter exponential‐type potential for diatomic molecules

“…This potential model has attracted much attention. [10][11][12][13][14][15][16][17][18][19] Ovando et al [10] showed that the MPETP includes some well-known diatomic potentials such as the Manning-Rosen potential, Schiöberg potential and Tietz potential as special cases. Yazarloo et al [11] solved the s-wave Schröinger equation with the MPETP and investigated the scattering amplitudes for several special cases.…”

“…Investigations of the bound and scattering states of the Schrödinger, Klein-Gordon, and Dirac equations for the MPETP in three and higher spatial dimensions have aroused considerable interest of many authors. [11][12][13][14][15][16][17][18] However, as far as we know, one has not reported any investigation on modeling internuclear interaction potential curves for real diatomic molecules by employing the MPETP. In addition, the MPETP still remains a fault without explicit physical definitions for the potential parameters.…”

“…In 2012, García‐Martínez et al constructed an exactly solvable multiparameter exponential‐type potential (MPETP) based on the canonical transformation method applied to a general second‐order differential equation. This potential model has attracted much attention . Ovando et al showed that the MPETP includes some well‐known diatomic potentials such as the Manning‐Rosen potential, Schiöberg potential and Tietz potential as special cases.…”

“…Ikot et al solved the D ‐dimensional Schröinger equation with the MPETP and discussed in detail the scattering and bound states. Bakhti et al investigated solutions of the Schröinger equation with the MPETP in terms of the Feynman path‐integral method. Ovando et al investigated in detail the supersymmetric properties of the MPETP.…”

“…Ovando et al investigated in detail the supersymmetric properties of the MPETP. Investigations of the bound and scattering states of the Schrödinger, Klein‐Gordon, and Dirac equations for the MPETP in three and higher spatial dimensions have aroused considerable interest of many authors . However, as far as we know, one has not reported any investigation on modeling internuclear interaction potential curves for real diatomic molecules by employing the MPETP.…”