The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

doi:10.1088/1674-1056/21/10/100303

Abstract We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix (ATM) method. A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation, which can be used to calculate the energies of higher rotational states from the energies of lower states. The energies of rotational states of the hydrogen molecule are calculated by the ATM condition, and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.

Keywords: rotating Morse potential analytical transfer matrix (ATM) Pekeris approximation supersymmetry quantum mechanics (SUSY QM)

Received: 22 February 2012
Revised: 19 March 2012
Accepted manuscript online:

PACS:	03.65.Sq	(Semiclassical theories and applications)
	03.65.Ge	(Solutions of wave equations: bound states)
	11.30.Pb	(Supersymmetry)

Fund: Project supported by the Fund front the Science and Technology Committee of Shanghai Municipality, China (Grant No. 11ZR1412300) and the National Natural Science Foundation of China (Grant No. 61108010).

Corresponding Authors: He Ying
E-mail: heying@staff.shu.edu.cn

Cite this article:

He Ying (何英), Tao Qiu-Gong (陶求功), Yang Yan-Fang (杨艳芳) The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method 2012 Chin. Phys. B 21 100303

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The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

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