Another set of infinitely many exceptional ( X ? ) Laguerre polynomials

摘要

We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X?) 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 correspondingX?Laguerre and Jacobi polynomials [S. Odake, R. Sasaki, Phys. Lett. B 679 (2009) 414]. The newX?Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the knownX?Jacobi polynomials and the potentials, whereas the knownX?Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the knownX?Jacobi polynomials and the potentials.