A three-body force model for the harmonic and anharmonic oscillator

We present a mathematical method to describe motion of a system based on 3 identical body forces. The 3-body forces are more easily introduced and treated within the hyperspherical harmonics. We have obtained an exact solution of the radial Schrödinger equation for a 3- body system in three dimensions. The interact potential V is assumed to depend on the hyperradius X only where X is a function of the Jacobi relative coordinates ρ and λ which are functions of the three identical particles, relative positions r12, r23 and r31. This method has been extensively used in nuclear and molecular physics. This work is interesting to those who are studying hadronic and bosonics physics and problems consisting three - body systems.