Quasi-exactly solvable systems and orthogonal polynomials

Journal Article · Mon Jan 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531373· OSTI ID:253458

Bender, C M ^[1]; Dunne, G V ^[2]

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1. Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
2. Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States)

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {l_brace}{ital P}{sub {ital n}}{r_brace}. The quantum-mechanical wave function is the generating function for the {ital P}{sub {ital n}}({ital E}), which are polynomials in the energy {ital E}. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index {ital n} exceeds a critical value {ital J}. The zeros of the critical polynomial {ital P}{sub {ital J}}({ital E}) are the quasi-exact energy eigenvalues of the system. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 253458
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 1 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
EIGENVALUES
ENERGY LEVELS
POLYNOMIALS
RECURSION RELATIONS
SCHROEDINGER EQUATION
WAVE FUNCTIONS
WEIGHTING FUNCTIONS