Abstract
Using the ``pseudo-invariant eigen-operator" method we find the energy-gap of the Jaynes–Cummings Hamiltonian model of an atom-cavity system. This model takes the atomic centre-of-mass motion into account. The supersymmetric structure is involved in the Hamiltonian of an atom-cavity system. By selecting suitable supersymmetric generators and using supersymmetric transformation the Hamiltonian is diagonalized and energy eigenvectors are obtained.