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Recently a $f$-deformed Fock space which is spanned by $|n>_{\lambda}$ hasbeen introduced. These bases are indeed the eigen-states of a deformednon-Hermitian Hamiltonian. In this contribution, we will use a rather newnon-orthogonal basis vectors for the construction of coherent and squeezedstates, which in special case lead to the earlier known states. For thispurpose, we first generalize the previously introduced Fock space spanned by$|n>_{\lambda}$ bases, to a new one, spanned by an extended two-parametersbases $|n>_{\lambda_{1},\lambda_{2}}$. These bases are now the eigen-states ofa non-Hermitian Hamiltonian$H_{\lambda_{1},\lambda_{2}}=a^{\dagger}_{\lambda_{1},\lambda_{2}}a+1/2$, where$a^{\dagger}_{\lambda_{1},\lambda_{2}}=a^{\dagger}+\lambda_{1}a + \lambda_{2}$and $a$ are respectively, the deformed creation and ordinary bosonicannihilation operators. The bases $|n>_{\lambda_{1},\lambda_{2}}$ arenon-orthogonal (squeezed states), but normalizable. Then, we deduce the newrepresentations of coherent and squeezed states, in our two-parameters Fockspace. Finally, we discuss the quantum statistical properties, as well as thenon-classical properties of the obtained states, numerically.

Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space