Pseudo-invariant Eigen-operator for Deriving Energy-Level Gap for Jaynes-Cummings Model

We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through ana-lyzing the standard Jaynes-Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric generators of this model, which diretly leads to the energy-level gap for Jaynes-Cummings Hamiltonian.