  The effects of two distinct operations of the elements of the symmetry groups
of a Hamiltonian on a quantum state might be equivalent in some specific zones
of coordinate space. Making use of the matrix representations of the groups,
the equivalence leads to a set of homogeneous linear equations imposing on the
wave functions. When the matrix of the equations is non-degenerate, the wave
functions will appear as nodal surfaces in these zones. Therefore, the
equivalence leads to the existence of inherent nodal structure in the quantum
states. In this paper, trapped 3-boson systems with different types of
interactions are studied. The structures of the tightly bound eigenstates have
been analyzed systematically. The emphasis is placed to demonstrate the
universality arising from the common inherent nodal structures.
