Induced entangled state representations for generating fractional Fourier–Hankel transform.

Based on the fact that the quantum mechanical version of Hankel transform kernel (the Bessel function) is just the transform between | q , r 〉 and (s , r ′ | , two induced entangled state representations, and working with them, we derive fractional Fourier–Hankel transformation (FrFHT) caused by the operator e − i α (a 1 † a 1 + a 2 † a 2) e i π a 2 † a 2 , where e i π a 2 † a 2 is named the core operator and is essential to the fractional transformation. The fractional property (additive rule) of the FrFHT can be explicitly proved. [ABSTRACT FROM AUTHOR]