Testing the symmetrization postulate on molecules with three identical nuclei

We propose an experiment to look for possible small violations of the symmetrization postulate of quantum mechanics, in systems composed of three identical particles. Such violations could be detected by investigating the population of particular rotovibrational states of symmetrical molecules containing three identical nuclei. We discuss the symmetry properties of such states, and the implications of the symmetrization postulate and the spin statistics connection. A high-sensitivity spectroscopic investigation of simple molecules such as SO3 , BH3 , and NH3 could lead, to our knowledge, to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.