Infinitely many shape invariant potentials and new orthogonal polynomials
Infinitely many shape invariant potentials and new orthogonal polynomials
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DOI：
10.1016/j.physletb.2009.08.004
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发表时间：
2009-05
影响因子：
4.4
通讯作者：
S. Odake;R. Sasaki
中科院分区：
文献类型：
--
作者：
S. Odake;R. Sasaki
给出了三组精确可解的一维量子力学势。这些是通过使径向振子和三角/双曲Pöschl-Teller势变形而获得的形状不变势。我们提出了整个本征函数的这些哈密尔顿算子（ε = 1，2，.）的新的正交多项式。两个最近报道的形状不变的潜力Quesne和戈麦斯Ullate等人。是这些无穷多个势能的第一个成员。
Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic Pöschl–Teller potentials in terms of their degree ℓ polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (ℓ=1,2,…) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and Gómez-Ullate et al.'s are the first members of these infinitely many potentials.