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

Couplings in coupled channels versus wave functions in the case of resonances: application to the two $\Lambda(1405)$ states