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

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