Two-body wave functions and compositeness from scattering amplitudes; General properties with schematic models

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. As a result, the two-body wave functions from the Lippmann-Schwinger equation coincides with that from the Schrodinger equation for an energy-independent interaction. Of special interest is that the two-body wave function from the scattering amplitude is automatically scaled; the norm of the two-body wave function, to which we refer as the compositeness, is unity for an energy-independent interaction, while the compositeness deviates from unity for an energy-dependent interaction, which can be interpreted to implement missing channel contributions.