Exactly Solvable Quantum Mechanics and Infinite Families of   Multi-indexed Orthogonal Polynomials
  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. 
Satoru Odake and Ryu Sasaki
math-ph hep-th math.CA math.MP nlin.SI quant-ph