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Step Operators for the Quasi-exactly Solvable Systems

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Abstract

In this paper, we investigate the step operators for the quasi-exactly solvable problems. We also discuss the commutation relations between the step operators and the Hamiltonian of the quasi-exactly solvable system. After obtaining the general results, we take the anharmonic oscillators with x 6 anharmonicity in quasi-exactly solvable problems as examples to give the specific forms of step operators.

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Acknowledgements

This work is supported in part by NSF of China under Grant No. 11075115, and also supported by the Scientific Research Foundation of Civil Aviation University of China (09qd02S).

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Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Liyan Liu

  2. College of Gemology and Material Technics, Shijiazhuang University of Economics, Shijiazhuang, 050031, China

    Liqian Wei

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  1. Liyan Liu
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  2. Liqian Wei
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Correspondence to Liyan Liu.

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Liu, L., Wei, L. Step Operators for the Quasi-exactly Solvable Systems. Int J Theor Phys 51, 3605–3613 (2012). https://doi.org/10.1007/s10773-012-1247-y

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  • DOI: https://doi.org/10.1007/s10773-012-1247-y

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