Lie algebras of differential operators and Lie-algebraic potentials

Niky Kamran, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


An explicit characterisation of all second order differential operators on the line which can be written as bilinear combinations of the generators of a finite-dimensional Lie algebra of first order differential operators is found, solving a problem arising in the Lie-algebraic approach to scattering theory and molecular dynamics. One-dimensional potentials corresponding to these Lie algebras are explicitly classified, which include the harmonic oscillator, Morse, one-soliton (Pöschl-Teller), Mathieu, Lamé, confluent hypergeometric, and Bessel potentials.

Original languageEnglish (US)
Pages (from-to)342-356
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Jan 15 1990

Bibliographical note

Funding Information:
* Research supported in part by NSF and NSERC grants. ’ Research supported in part by the NSF under Grant DMS 86-02004.


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