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This paper is dedicated to finding the quadrature operator eigenstates andwavefunctions of the most general $f$-deformed oscillators. A definition forquadrature operator for deformed algebra is derived to obtain the quadratureoperator eigenstates. A new set of polynomials are obtained using thisquadrature operator and these polynomials are used to find explicitly thewavefunctions of the deformed oscillators. We have plotted wavefunctions forthree different types of deformations and compared it with the wavefunctions ofthe non-deformed oscillator. Our result will immensely help the research groupsworking in the quantum state reconstruction and quantum information theory ofdeformed states.

Quadrature operator eigenstates and wavefunctions of $f$-deformed oscillators