Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
arXiv:1105.0508 · doi:10.1016/j.physletb.2011.06.075
Abstract
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of type I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the `virtual state wavefunctions' which are `deleted' by the generalisation of Crum-Adler theorem. Each polynomial has another integer n which counts the nodes.
7 pages, 1 figure. Comments and references added. Typo corrected(4,5 lines below eq.(5)). To appear in Phys.Lett.B