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.
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