Lie algebras of differential operators and Lie-algebraic potentials
Niky Kamran,Peter J. Olver +1 more
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TLDR
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.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1990-01-15 and is currently open access. It has received 121 citations till now. The article focuses on the topics: Lie conformal algebra & Adjoint representation of a Lie algebra.read more
Citations
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Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
TL;DR: In this paper, the authors completely determine necessary and sufficient conditions for the normalizability of wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrodinger operator on the line.
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Ladder operators and differential equations for orthogonal polynomials
Yang Chen,Mourad E. H. Ismail +1 more
TL;DR: In this paper, the authors derived raising and lowering differential recurrence relations for polynomials orthogonal with respect to a weight function supported in the real line under some integrability conditions.
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Lie algebras of vector fields in the real plane
TL;DR: Finite-dimensional real analytic Lie algebras of vector fields on R 2 are completely classified up to changes of local coordinates as mentioned in this paper, and they can be classified in two different ways.
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Nonlinear supersymmetric quantum mechanics: concepts and realizations
TL;DR: The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed in this paper, its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described.
References
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Book
Special Functions and the Theory of Group Representations
TL;DR: In this paper, a standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special function are related to (and derived from) simple well-known facts of representation theory.
BookDOI
Differentialgleichungen : Lösungsmethoden und Lösungen
TL;DR: A molded plastic bowling pin incorporating a core extending the length of the pin substantially from its base to its head and constituted of a plurality of plastic core elements of varying sizes and shapes such that the composite pin incorporating the same meets the weight distribution standards set by the American Bowling Congress, and a shell having a substantially uniform thickness about the core elements and being integrally molded on and firmly bonded thereto.
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Theorie der Transformationsgruppen
TL;DR: In this paper, the authors present a general theory of the Beruhrungstransformationen and the Gruppen von Beruhrasformationen (GBSs) in the context of continuirlichen Transformationsgruppen.
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Invariants of real low dimension Lie algebras
TL;DR: In this paper, all invariant functions of the group generators (generalized Casimir operators) are found for real algebras of dimension up to five and for all real nil-potent algebras of dimension six.