A bosonized formulation of the supersymmetric quantum mechanics for shape-invariant potential systems

We consider the minimal bosonization realization of supersymmetric shape-invariant systems where generalized supercharge operators are constructed using the partner supersymmetric operators, the parameter potential translation formalism and the reflection operator. We obtain the solution of the eigenvalue equation and study the quantum dynamics of the supersymmetric system including terms in the Hamiltonian which are constructed using the combination of the bosonized supercharge operators. The connections between the bosonized supersymmetric formalism, the Bose-Fermi transformation and the generalization of the -deformed Heisenberg algebra are discussed. As an illustration, we apply the generalized formalism for the case of the trigonometric Rosen-Morse potential.