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

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

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120304-120304.doi: 10.1088/1674-1056/20/12/120304

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

桑明煌, 余子星, 李翠翠, 涂凯

Department of Physics, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2010-05-09 修回日期:2011-06-20 出版日期:2011-12-15 发布日期:2011-12-15
基金资助:
Project supported by the State Key Laboratory of Advanced Optical Communication Systems and Networks of China (Grant No. 2008SH05).

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

Sang Ming-Huang(桑明煌)^†, Yu Zi-Xing(余子星), Li Cui-Cui(李翠翠), and Tu Kai(涂凯)

Department of Physics, Jiangxi Normal University, Nanchang 330022, China

Received:2010-05-09 Revised:2011-06-20 Online:2011-12-15 Published:2011-12-15
Supported by:
Project supported by the State Key Laboratory of Advanced Optical Communication Systems and Networks of China (Grant No. 2008SH05).

摘要/Abstract

摘要： 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.

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.

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

中图分类号: (Semiclassical theories and applications)

03.65.Sq

11.30.Pb (Supersymmetry)

桑明煌, 余子星, 李翠翠, 涂凯. Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method[J]. 中国物理B, 2011, 20(12): 120304-120304.

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[J]. Chin. Phys. B, 2011, 20(12): 120304-120304.

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

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

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