Infinitely many shape invariant potentials and new orthogonal polynomials

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• 作者：Satoru Odake ; Ryu Sasaki
• 关键词：Shape invariance ; Orthogonal polynomials
• 刊名：Physics Letters B
• 出版年：2009
• 出版时间：31 August 2009
• 年：2009
• 卷：679
• 期：4
• 页码：414-417
• 全文大小：160 K

文摘

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.