  The multiphoton algebras for one-dimensional Hamiltonians with infinite
discrete spectrum, and for their associated kth-order SUSY partners are
studied. In both cases, such an algebra is generated by the multiphoton
annihilation and creation operators, as well as by Hamiltonians which are
functions of an appropriate number operator. The algebras obtained turn out to
be polynomial deformations of the corresponding single-photon algebra
previously studied. The Barut-Girardello coherent states, which are eigenstates
of the annihilation operator, are obtained and their uncertainty relations are
explored by means of the associated quadratures.
