  Quantum states of systems made of many identical particles, e.g. those
described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted
in the Fock space. However, in order to evaluate some specific observables or
to study the system dynamics, it is often more effective to employ the Hilbert
space description. Moving effectively from one description to the other is thus
a desirable feature, especially when a numerical approach is needed. Here we
recall the construction of the Fock space for systems of indistinguishable
particles, and then present a set of recipes and advices for those students and
researchers in the need to commute back and forth from one description to the
other. The two-particle case is discussed in some details and few guidelines
for numerical implementations are given.
