Abstract

We define a discrete Bargmann transform for discrete and finite functions by means of the coherent states in the su(2) finite harmonic oscillator model. The transform space is over a corresponding finite square mesh in the complex plane. From there, the inverse discrete Bargmann transform reconstitutes the original function with an average error of 107 for functions of unit norm. Three defining properties of the Bargmann transform also hold in this discrete version: (1) the Bargmann transform of finite su(2) harmonic oscillator functions are complex power functions; (2) the discrete su(1,1) repulsive oscillator functions self-reproduce in the chosen finite interval with little error; and (3) the oscillator dynamics under the fractional Fourier transform in Bargmann’s complex space correspond, in this discrete transform, to the dynamics under the su(2) fractional Fourier–Kravchuk transform.

© 2019 Optical Society of America

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