  The Bethe-Salpeter wave functions of $SU(3)$ pure gauge glueballs are
revisited in this study. The ground and the first excited states of scalar and
tensor glueballs are identified unambiguously by using the variational method
on the basis of large operator sets. We calculate their wave functions in the
Coulomb gauge and use two lattices with different lattice spacings to check the
discretization artifacts. For ground states, the radial wave functions are
approximately Gaussian and the size of the tensor is twice as large as that of
the scalar. For the first excited states, the radial nodes are clearly observed
for both the scalar and the tensor glueballs, such that they can be interpreted
as the first radial excitations. These observations may shed light on the
theoretical understanding of the inner structure of glueballs.
