  In this paper we develop a formalism to evaluate wave functions in momentum
and coordinate space for the resonant states dynamically generated in a unitary
coupled channel approach. The on shell approach for the scattering matrix,
commonly used, is also obtained in Quantum Mechanics with a separable
potential, which allows one to write wave functions in a trivial way. We
develop useful relationships among the couplings of the dynamically generated
resonances to the different channels and the wave functions at the origin. The
formalism provides an intuitive picture of the resonances in the coupled
channel approach, as bound states of one bound channel, which decays into open
ones. It also provides an insight and practical rules for evaluating couplings
of the resonances to external sources and how to deal with final state
interaction in production processes. As an application of the formalism we
evaluate the wave functions of the two $\Lambda(1405)$ states in the $\pi
\Sigma$, $\bar{K} N$ and other coupled channels.
