Abstract
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 language | English (US) |
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Pages (from-to) | 342-356 |
Number of pages | 15 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 145 |
Issue number | 2 |
DOIs | |
State | Published - 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.