ALGEBRAIC AND SPECTRAL PROPERTIES OF SOME QUASI-ORTHOGONAL POLYNOMIALS ENCOUNTERED IN QUANTUM RADIATION

The nodal structure of the wavefunctions of a large class of quantum-m echanical potentials is often governed by the distribution of zeros of real quasiorthogonal polynomials. It is known that these polynomials (i) may be described by an arbitrary linear combination of two orthogo nal polynomials {P-n(x)} and (ii) have real and simple zeros. Here, th e three term recurrence relation, the second order differential equati on and the distribution of zeros of quasiorthogonal polynomials of the classical class (i.e., when P-n(x) is a Jacobi, Laguerre or Hermite p olynomial) are derived and analyzed. Specifically, the exact values of the Newton sum rules and the WKB density of zeros of these polynomial s are found. (C) 1995 American Institute of Physics.