  The existence of bound state of the polarizable neutral atom in the inverse
square potential created by the electric field of single walled charged carbon
nanotube (SWNT) is shown to be theoretically possible. The consideration of
inequivalent boundary conditions due to self-adjoint extensions lead to this
nontrivial bound state solution. It is also shown that the scaling anomaly is
responsible for the existence of bound state. Binding of the polarizable atoms
in the coupling constant interval \eta^2\in[0,1) may be responsible for the
smearing of the edge of steps in quantized conductance, which has not been
considered so far in literature.
