Three-body bound states of two bosons and one impurity in one dimension

We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body zero-range interactions. For the case in absence interaction, we give a complete phase diagram number bound states whole region mass ratio via direct calculation Skornyakov-Ter-Martirosyan equations. demonstrate that other low-lying emerge when impurity particle is not equal to another particles. can obtain only binding energies but also corresponding wave functions. When vary large, there are at most three states. then study effect interaction unveil it induces more state certain coupling strength under fixed ratio.