The dispersive approximation (or limit) in the context of the Jaynes-Cummings model is an approximation that assumes that the detuning between the transition frequency of the two-level system and the cavity mode is large compared to the coupling strength between them. In this approximation, the coupling strength can be treated as a small perturbation, and the interaction Hamiltonian can be approximated as a time-independent Hamiltonian. This approximation is useful for calculating the energy levels of the system, as well as the associated energies and wavefunctions for the field and the two-level system.