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Quasi exactly solvable operators and abstract associative algebras

Journal Article · · AIP Conference Proceedings
DOI:https://doi.org/10.1063/1.57095· OSTI ID:21202645
;  [1]
  1. Department of Mathematical Physics, University of Mons-Hainaut, Mons (Belgium)
We consider the vector spaces consisting of direct sums of polynomials of given degrees and we show how to classify the linear differential operators preserving these spaces. The families of operators so obtained are identified as the envelopping algebras of particular abstract associative algebras. Some of these operators can be transformed into quasi exactly solvable Schroedinger operators which, having a hidden algebra, can be partially solved algebraically; we exhibit however a series of Schoedinger equations which, while completely solvable algebraically, do not possess a hidden algebra.
OSTI ID:
21202645
Journal Information:
AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 453; ISSN APCPCS; ISSN 0094-243X
Country of Publication:
United States
Language:
English

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