The paper gives recurrence-based expressions for f-deformed oscillator quadrature wavefunctions, but leaves the ground state undetermined, so the wavefunctions are not explicit.
Marnelius, Acta Phys
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Quadrature operator eigenstates and wavefunctions of $f$-deformed oscillators
The paper gives recurrence-based expressions for f-deformed oscillator quadrature wavefunctions, but leaves the ground state undetermined, so the wavefunctions are not explicit.