  We demonstrate that quantum Hamiltonian operator for a free transverse field
within the framework of the second quantization reveals an alternative set of
states satisfying the eigenstate functional equations. The construction is
based upon extensions of the quadratic form of the transverse Laplace operator
which are used as a source of spherical basis functions with singularity at the
origin. This basis then naturally takes place of the one of plane or spherical
waves in the process of Fourrier or spherical variable separation.
