Quasi-Exactly Solvable Systems and Orthogonal Polynomials

Abstract

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.

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

References in corpus (2)

• Continued Fraction as a Discrete Nonlinear Transform
• Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line

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