Open Access
March 2011 Shape invariant potentials in second-order supersymmetric quantum mechanics
Wang-Chang Su
J. Phys. Math. 3: 1-12 (March 2011). DOI: 10.4303/jpm/P110502


Shape invariance condition in the framework of second-order supersymmetric quantum mechanics is studied. Two classes of solvable shape invariant potentials are consequently constructed, in which the parameters $a_0$ and $a_1$ of partner potentials are related to each other by translation $a_1 = a_0 + \alpha$. In each class, general properties of the obtained shape invariant potentials are systematically investigated. The energy eigenvalues are algebraically determined and the corresponding eigenfunctions are expressed in terms of generalized associated Laguerre polynomials. It is found that these shape invariant potentials are inherently singular, characterized by the $1/x^2$ singularity at the origin.


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Wang-Chang Su. "Shape invariant potentials in second-order supersymmetric quantum mechanics." J. Phys. Math. 3 1 - 12, March 2011.


Published: March 2011
First available in Project Euclid: 22 September 2011

zbMATH: 1264.81228
Digital Object Identifier: 10.4303/jpm/P110502

Primary: 81Q60 , 81Q80

Keywords: quantum theory , Special quantum systems , supersymmetry

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
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