RT Journal Article
T1 Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
A1 Gómez-Ullate Otaiza, David
A1 Grandati, Yves
A1 Milson, Robert
AB We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux-Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2m, and they are indexed by the partitions λ of m. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2l + 3 recurrence relation where l is the length of the partition λ. Explicit expressions for such recurrence relations are given.
PB IOP Publishing Ltd
SN 1751-8113
YR 2014
FD 2014-01-10
LK https://hdl.handle.net/20.500.14352/34707
UL https://hdl.handle.net/20.500.14352/34707
LA eng
NO © IOP Publishing Ltd.The research of the first author (DGU) has been supported in part by Spanish MINECO-FEDER grants MTM2009-06973, MTM2012-31714, and the Catalan grant 2009SGR-859. The research of the third author (RM) was supported in part by NSERC grant RGPIN-228057-2009.
NO Spanish MINECO-FEDER
NO Catalan
NO NSER
DS Docta Complutense
RD 7 abr 2025