Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials

By Satoru Odake, Ryu Sasaki. 2009

141 citations recorded by the source corpus.

Abstract We present a new set of infinitely many shape invariant potentials and the corresponding exceptional ( X l ) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one-dimensional quantum mechanics and the corresponding X l Laguerre and Jacobi polynomials [S. Odake, R. Sasaki, Phys. Lett. B 679 (2009) 414]. The new X l Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X l Jacobi polynomials and the potentials, whereas the known X l Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the known X l Jacobi polynomials and the potentials.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f62678bf60ecb953f05dfd57bb3ebac411256be7

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In Applied Mathematics

1. Satoshi Tsujimoto
2. Alexei S. Zhedanov
3. Ryu Sasaki
4. V. Spiridonov
5. Paul M. Terwilliger

In Atomic and Molecular Physics, and Optics

1. Satoshi Tsujimoto
2. Alexei S. Zhedanov
3. Ryu Sasaki
4. Antonio J. Dur'an
5. V. Spiridonov
6. Paul M. Terwilliger

In Statistical and Nonlinear Physics

1. Satoshi Tsujimoto
2. Alexei S. Zhedanov
3. Ryu Sasaki
4. Antonio J. Dur'an
5. V. Spiridonov
6. Paul M. Terwilliger

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].”