@article{gomez-ullateRationalExtensionsQuantum2014,
 abstract = {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 2 m, and they are indexed by the partitions $łambda$ 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 2$\ell$ + 3 recurrence relation where $\ell$ is the length of the partition $łambda$. Explicit expressions for such recurrence relations are given.},
 author = {Gómez-Ullate, David and Grandati, Yves and Milson, Robert},
 copyright = {http://iopscience.iop.org/info/page/text-and-data-mining},
 doi = {10.1088/1751-8113/47/1/015203},
 file = {/Users/david/Zotero/storage/64WA4LBX/Gómez-Ullate et al. - 2014 - Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.pdf},
 issn = {1751-8113, 1751-8121},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 month = {January},
 number = {1},
 pages = {015203},
 title = {Rational Extensions of the Quantum Harmonic Oscillator and Exceptional Hermite Polynomials},
 urldate = {2025-10-19},
 volume = {47},
 year = {2014}
}