Quasi exactly solvable operators and abstract associative algebras

Details Quasi exactly solvable operators and abstract associative algebras Quasi exactly solvable operators and abstract associative algebras

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aipc..453..177b&link_type=abstract

Particles, fields and gravitation. AIP Conference Proceedings, Volume 453, pp. 177-185 (1998).

Computer Science

Theory Of Quantized Fields, Field Theory, Solutions Of Wave Equations: Bound States, Algebraic Methods

Scientific paper

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.

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