Quasi-Exactly Solvable Systems and Orthogonal Polynomials

Details Quasi-Exactly Solvable Systems and Orthogonal Polynomials Quasi-Exactly Solvable Systems and Orthogonal Polynomials

1995-11-20

arxiv.org/abs/hep-th/9511138v1

J.Math.Phys. 37 (1996) 6-11

Physics

High Energy Physics

High Energy Physics - Theory

9pp, RevTeX, no figures; to appear in J. Math. Phys

Scientific paper

10.1063/1.531373

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials $\{ P_n\}$. The quantum-mechanical wave function is the generating function for the $P_n (E)$, which are polynomials in the energy $E$. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index $n$ exceeds a critical value $J$. The zeros of the critical polynomial $P_J(E)$ are the quasi-exact energy eigenvalues of the system.

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