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Two-body wave functions and compositeness from scattering amplitudes

Sekihara, Takayasu

For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole, by considering solutions of both the Schr$"{o}$dinger and Lippmann-Schwinger equations. This means that solving the Lippmann-Schwinger equation at the bound state pole is equivalent to evaluating the two-body wave function of the bound state. We apply this method to candidates of hadronic molecules such as $$Lambda (1405)$$ described in hadron-hadron scattering amplitudes in hadron effective models and calculate the compositeness as the norm of the two-body wave function.

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