  Eigenvalues and eigenfunction of two-boson 2x2 Hamiltonians in the framework
of the superalgebra osp(2,1) are determined by presenting a similarity
transformation. The Hamiltonians include two bosons and one fermion have been
transformed in the form of the one variable differential equations and the
conditions for its solvability have been discussed. It is observed that the
Hamiltonians of the various physical systems can be written in terms of the
generators of the osp(2,1) superalgebra and under some certain conditions their
eigenstates can exactly be obtained. In particular, the procedure given here is
useful in determining eigenstates of the Jaynes-Cummings Hamiltonians.
