  In this paper the factorization method is used in order to obtain the
eigenvalues and eigenfunctions of a quantum particle confined in a
one-dimensional infinite well. The output results from the mentioned approach
allows us to explore an appropriate new pair of raising and lowering operators
corresponding to the physical system under consideration. From the symmetrical
considerations, the connection between the obtained ladder operators with
$su(1,1)$ Lie algebra is explicitly established. Next, after the construction
of Barut-Girardello and Gilmore-Perelomov representations of coherent states
associated with the considered system, some of their important properties like
the resolution of the identity including a few nonclassical features are
illustrated in detail. Finally, a theoretical scheme for generation of the
Gilmore-Perelomov type of coherent state via a generalized Janes-Cummings model
is proposed.
