Based on the linear quantum transformation theory, we further propose a sup
ersymmetric unitary transformation, whose operator can be constructed by th
e supersymmetric generators of Lie superalgebra. Therefore, by making use o
f the supersymmetric unitary transformation, we can obtain the eigenspectru
m, the eigenstates and the super-partition function for the Super-Jaynes-Cu
mmings model when the coupling constants are Grrassmann valued.