  Using a similarity transformation that maps the Calogero model into $N$
decoupled quantum harmonic oscillators, we construct a set of mutually
commuting conserved operators of the model and their simultaneous
eigenfunctions. The simultaneous eigenfunction is a deformation of the
symmetrized number state (bosonic state) and forms an orthogonal basis of the
Hilbert (Fock) space of the model. This orthogonal basis is different from the
known one that is a variant of the Jack polynomial, i.e., the Hi-Jack
polynomial. This fact shows that the conserved operators derived by the
similarity transformation and those derived by the Dunkl operator formulation
do not commute. Thus we conclude that the Calogero model has two, algebraically
inequivalent sets of mutually commuting conserved operators, as is the case
with the hydrogen atom. We also confirm the same story for the $B_{N}$-Calogero
model.
