Fractional Hankel transform studied by charge-amplitude state representations and complex fractional Fourier transformation.
Starting from a complex fractional Fourier transformation [Opt. Lett. 28, 680 (2003)], it is shown that the integral kernel of a fractional Hankel transformation is equivalent to the matrix element of an appropriate operator in the charge-amplitude state representations; i.e., the fractional Hankel transformation is endowed with a definite physical meaning (definite quantum-mechanical representation transform).
Fan
Hong-yi
HY
Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China. fhym@ustc.edu.cn