Onq-extended eigenvectors of the integral and finite Fourier transforms

N M Atakishiyev, J P Rueda, K B Wolf
2007 Journal of Physics A: Mathematical and Theoretical  
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 of
more » ... ns of eigenfunctions of the Fourier integral transform.
doi:10.1088/1751-8113/40/42/s14 fatcat:usckah3hjvdcnmdwe2rkuqipti