Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

doi:10.1088/1674-1056/20/12/120304

Abstract For the conventional translational shape-invariant potentials (TSIPs), it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.

Keywords: translational shape-invariant potentials supersymmetric quantum mechanics analytical transfer matrix method scattered subwaves generating function

Received: 09 May 2010
Revised: 20 June 2011
Accepted manuscript online:

PACS:	03.65.Sq	(Semiclassical theories and applications)
	11.30.Pb	(Supersymmetry)

Fund: Project supported by the State Key Laboratory of Advanced Optical Communication Systems and Networks of China (Grant No. 2008SH05).

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Sang Ming-Huang(桑明煌), Yu Zi-Xing(余子星), Li Cui-Cui(李翠翠), and Tu Kai(涂凯) Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method 2011 Chin. Phys. B 20 120304

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Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

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