The Bertlmann-Martin Inequalities in the Three-Body Problem

The Bertlmann-Martin inequalities (BMI) are studied in the three-body case. We consider distinguishable particles and scalar interactions. The systems are described by Schrodinger equations with local potentials. Under these conditions we show that the lower bound character of the BMI is preserved. We discuss the question of the correction factors transforming the inequalities into approximate or exact relationships. As illustrative example, a simple model in the (D = 1)-dimensional space is considered, for which the exact solution is known. We also study what can be learned from the Hartree approximation and the hyperspherical method in the central potential approximation with respect to the BMI inequalities and correction factors.