ar X iv : h ep - t h / 94 12 11 6 v 1 1 3 D ec 1 99 4 Quantum transfer matrices for discrete and continuous quasi - exactly solvable problems

ar X iv : h ep - t h / 94 12 15 6 v 1 1 8 D ec 1 99 4 Quantal Overlapping Resonance Criterion : the Pullen Edmonds Model

ar X iv : h ep - t h / 94 12 09 9 v 1 1 2 D ec 1 99 4 Poisson Poincaré groups

We present almost complete list of normal forms of classical r-matrices on the Poincaré group.

ar X iv : h ep - t h / 94 12 02 2 v 1 2 D ec 1 99 4 Interacting anyons and the Darwin Lagrangian

We propose a new model for interacting (electrically charged) anyons, where the 2+1-dimensional Darwin term is responsible for interactions. The Hamiltonian is comparable with the one used previously (in the RPA calculation).

ar X iv : h ep - t h / 96 11 22 6 v 1 2 7 N ov 1 99 6 On the relations between osp ( 2 , 2 ) and the quasi exactly solvable systems

By taking a product of two sl(2) representations, we obtain the differential operators preserving some space of polynomials in two variables. This allows us to construct the representations of osp(2,2) in terms of matrix differential operators in two variables. The corresponding operators provide the building blocks for the construction of quasi exactly solvable systems of two and four equation...

ar X iv : h ep - t h / 95 08 02 2 v 1 4 A ug 1 99 5 UICHEP - TH / 95 - 5 Methods for Generating Quasi - Exactly Solvable Potentials

We describe three different methods for generating quasi-exactly solvable potentials, for which a finite number of eigenstates are analytically known. The three methods are respectively based on (i) a polynomial ansatz for wave functions; (ii) point canonical transformations; (iii) supersymmetric quantum mechanics. The methods are rather general and give considerably richer results than those a...