Watson transform in quantum scattering

The scattering of high-energy quantum particles by nanoinclusions into crystalline lattices is studied. Since the typical size of the grid impurity is much larger compared to the wavelength of the produced matter waves, the canonical solutions for the wave functions given as series of spatial harmonics, converge very poorly. Therefore, Watson transform is employed to provide equivalent series that involve complex-ordered Hankel functions and possess a hugely better convergence rate. In this way, the use of a versatile tool is demonstrated allowing for rigorously solving and understanding particle interactions that occur within various research domains: from quantum emission and interference to molecular fluctuations and quantum signal processing.