The supercoherent state of the OSP(2,1) superalgebra is constructed and its
properties are discussed in detail. An inhomogeneous differential realizat
ion of the OSP(2, 1) superalgebra on the supercoherent- state space is give
n. It may be of use for determining new concrete structure of the quasi-exa
ctly-solvable Hamiltonian corresponding to the OSP(2,I) supersymmetric quan
tum system. (C) 2001 Elsevier Science B.V. All rights reserved.