Infinitely many shape invariant potentials and new orthogonal polynomials
By Satoru Odake, Ryu Sasaki. 2009
243 citations recorded by the source corpus.
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 Poschl-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 Gomez-Ullate et al.'s are the first members of these infinitely many potentials.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6d6e57b441bf1cdd92e8fb5a710f924597fa0284
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations (2010, methodology): “The additional term is the logarithm of the degree l eigenpolynomial, the Laguerre or Jacobi polynomial with twisted parameters or arguments, introduced by Odake-Sasaki [1, 2, 10].”
- Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials (2014, background): “The last few years have seen a great deal of activity in the area of exceptional and exceptional discrete orthogonal polynomials (see, for instance, [5, 8, 9, 15], [16] (where the adjective exceptional for this topic was introduced), [17, 18, 19, 20, 21, 26, 29, 30, 32, 36, 37, 39] and the reference”