Models for supersymmetric quantum-mechanics

An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The examples of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.