Eur. Phys. J. Plus (2016) 131: 2
https://doi.org/10.1140/epjp/i2016-16002-2

Regular Article

Stability analysis of the solution of the Dirac equation for the vibrational energies of the SiF⁺ molecule

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, Chengdu, PRC

^* e-mail: chshjia@263.net

Received: 28 August 2015
Accepted: 16 November 2015
Published online: 7 January 2016

Abstract

Analytical solutions of the Dirac equation with the spin symmetry in higher spatial dimensions have been explored for the improved Manning-Rosen potential energy model. We present the bound-state energy equation and the corresponding upper and lower radial wave functions. It has been found that the behavior of the higher-dimensional relativistic vibrational energies remains similar to that of the three-dimensional molecular system for the state of the SiF⁺ molecule. This symmetry phenomenon will break upon the critical point through which the system undergoes a phase transition from a stable to an unstable state.