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

Understand

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.