Abstract
Recently we proposed an exact transformation of the three-body Schrodinger operator in the form usually applied in the Born-Oppenheimer method. This transformation removed all the shortcomings of the Born-Oppenheimer method associated with an incorrect behaviour of an approximate solution in the regions of pair and triple collisions. In the present paper the relation of the new method with the adiabatic hyperspherical approach, which was successfully applied to study the He atom and theeee+ ion, is pointed out. The weakly bound state of thedtμ− ion is used as an example to demonstrate the advantages of the new approach in calculating also molecular systems. It is argued that the proposed method, which represents a natural combination of the two well-known approaches, is well applicable to solve a wide spectrum of fewbody problems.
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