  The motion of a muon in two centers coulomb field is one of the interesting
problems of quantum mechanics. The adiabatic expansion method is powerful
approach to study the muonic three-body system. In this investigation the
three-body problem is studied for short-range interactions. Bound states and
energy levels of this system were calculated and compared with their
Born-Oppenheimer method counterparts. The obtained results are in good
agreement with the previous calculations.
