Eur. Phys. J. Plus (2014) 129: 264
https://doi.org/10.1140/epjp/i2014-14264-2

Regular Article

Molecular spinless energies of the improved Rosen-Morse potential energy model in D dimensions

¹ State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 610500, Chengdu, People’s Republic of China
² College of Sciences, Southwest Petroleum University, 610500, Chengdu, People’s Republic of China
³ Scientific Research Office, Southwest Petroleum Institute, 610500, Chengdu, People’s Republic of China

^* e-mail: swputms@163.com

Received: 13 May 2014
Revised: 20 October 2014
Accepted: 28 October 2014
Published online: 15 December 2014

Abstract

Under the circumstance of equal scalar and vector potentials, we solve the Klein-Gordon equation with the improved Rosen-Morse potential energy model in D spatial dimensions. The relativistic bound state energy equation has been obtained by using the supersymmetric WKB approximation approach. For fixed vibrational quantum number and various rotational quantum numbers, the relativistic energies for the 3³ Σ _g ⁺ state of the Cs₂ molecule and the 5¹ Δ _g state of the Na₂ molecule increase as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.