TY - JOUR
T1 - Real Lie algebras of differential operators and quasi-exactly solvable potentials
AU - González-López, Artemio
AU - Kamran, Niky
AU - Olver, Peter
PY - 1996/5/15
Y1 - 1996/5/15
N2 - We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators in ℝ2. Furthermore, we find all algebras which are quasi-exactly solvable, along with the associated finite-dimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schrödinger operators on ℝ2.
AB - We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators in ℝ2. Furthermore, we find all algebras which are quasi-exactly solvable, along with the associated finite-dimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schrödinger operators on ℝ2.
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U2 - 10.1098/rsta.1996.0044
DO - 10.1098/rsta.1996.0044
M3 - Article
AN - SCOPUS:3142619242
SN - 1364-503X
VL - 354
SP - 1165
EP - 1193
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 1710
ER -