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

Recently, $f$-oscillators in its various forms have been recognised as extremely important tools in many branches of physics. This paper is dedicated to find the wavefunctions for the most general $f$-deformed oscillators. In the process, the homodyne quadrature operator and its eigenfunctions for the $f$-deformed case is obtained. Then the wavefunctions for deformed oscillators are obtained for different types of deformations and for each deformation the wavefunctions are obtained for different values of deformation. We have compared the deformed oscillator wavefunctions with the non-deformed oscillator.