Quasi exactly solvable operators and Lie superalgebras
arXiv:quant-ph/0211018 · doi:10.1016/S0375-9601(02)01636-5
Abstract
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. An example of a Hamiltonian possessing such a hidden algebra is analyzed.
8 Revtex pages, 1 PS-figures; Section IV extended, reference added