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Mehta has shown that eigenvectors of the N × N finite Fourier transform can be written in terms of the standard Hermite eigenfunctions of the quantum harmonic oscillator (1987 J. Math. Phys. 28 781). Here, we construct a oneparameter family of q-extensions of these eigenvectors, based on the continuous q-Hermite polynomials of Rogers. In the limit when q → 1 these q-extensions coincide with Mehta's eigenvectors, and in the continuum limit as N → ∞ they give rise to q-extensions ofdoi:10.1088/1751-8113/40/42/s14 fatcat:usckah3hjvdcnmdwe2rkuqipti