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Quasi exactly solvable (QES) equations with multiple algebraisations
Yves Brihaye, Betti Hartmann
We review three examples of quasi exactly solvable (QES) Hamitonians which possess multiple algebraisations. This includes the most prominent example, the Lame equation, as well as…
Quasi exactly solvable operators and Lie superalgebras
Yves Brihaye, Betti Hartmann
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…
Multiple algebraisations of an elliptic Calogero-Sutherland model
Yves Brihaye, Betti Hartmann
Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that t…
Quasi Exactly Solvable NxN-Matrix Schroedinger Operators
Yves Brihaye, Betti Hartmann
New examples of matrix quasi exactly solvable Schroedinger operators are constructed. One of them constitutes a matrix generalization of the quasi exactly solvable anharmonic oscil…