Lee-Low-Pine transformation and its generalization

In general, the analysis of few-body systems is a difficult task. Fortunately, some of these systems can be simplified through center-of-mass separation. While the center-of-mass coordinates are uniquely determined, there are multiple ways to define the coordinates for the relative motion. Whichever of them is best suited depends on the analyzed system. In the case of the impurity problem, a beneficial change of the coordinates can be performed using the Lee-Low-Pine (LLP) transformation. Unfortunately, this transformation works only for systems without external trapping potential. In the talk, I will present a modified version of LLP transformation, which can be used for any system with a separable center of mass.