Exact Results in Quantum Theory

Many body problem plays a central role in many physics sciences including celestial mechanics, atomic-molecular physics, nuclear physics. Its main characteristics is that the potential in both non-relativistic CM and QM de-pends on relative distances between bodies alone being translation-invariant.A new concept is proposed: to study particular solutions of n-body problem,both classical and quantum, which depend on relative distances ALONE. In such a case n-body problem becomes less dimensional and equivalent to ei-ther classical/quantum top in constant magnetic field or to multi-dimensional particle moving in curved space with some remarkable cometric. Since the ground state function — the main object in quantum mechanics — and choreography in classical mechanics are functions of relative distances ONLY they can be treated in much simpler way then up to now. Analogue of kineticenergy is (Lie)-algebraic operator which can be written in terms of sl(n(n+1)/2) algebra generators. Solvable but non-integrable 3-body harmonic oscillator might be briefly discussed.