where τ τ = ∫ ∫ d t ′ f 2 ( t ′ ) and the integral is over the duration of the interaction. Using the identity for Bessel functions of the first kind, e i α α cos ⁡ ⁡ ( β β ) = ∑ ∑ n = − − ∞ ∞ ∞ ∞ i n J n ( α α ) e i n β β , the above wavefunction becomes