Continuing this off-topic discussion, I was wondering if I could ask a question which has been on my mind lately. It is my understanding that the wavelength of a particle is inversely related to its momentum, and that therefore, in an accelerator, where both the velocity and the mass of the particles are continualy increasing, the wave aspect of the particle becomes less noticeable. But is there any way in which the wave nature of matter has been or potentially can be exploited in HEP experiments?
The answer is yes and no, depending on the context of your question. In the broad setting of the lab, particles in HEP behave very specifically like particles, as their wavelength is so small. Remember, though, that high-energy particles are used to probe tiny distances in collisions, where the wave properties of matter are inextricable from the particle properties. (Actually, relativistic QM, or quantum field theory, is used to understand the properties of these collisions. QFT calculations are very esoteric; the quantum mechanical "structure" of particles is inherent in it and the "wave" and "particle" aspects can't really be explicitly extricated.)
In low-energy physics (a whole other equally important, though less sensationalistic) subfield, approximating particles in scattering experiments as waves is done using partial wave analysis all the time.