Quantum Mechanics

Condensation, or collapse of the wave packet, has been mysterious in quantum mechanics since its earliest days. Mathematicians axiomatize it. We begin by applying special relativity to compare the wave packets for the massless photon with the massive electron. The comparison provides fresh understanding for Uncertainty and for dynamics that are written in terms of dispersion in wave mechanics. The wave-group contains two velocities that are verified by 100 years of consistent electron microscope measurements. The momenta of both massless and massive particles are compared. The momentum quanta in quasicrystals have extraordinary properties that demonstrate not only the structure of the 3-dimensional hierarchic solids, but also the nature of the quanta that are used to prove it. In the quasicrystal, the harmonies are dual: The probe is linear; the structure and diffraction patterns are geometric...all quanta are created by harmonies in space and time. The relativistic wave-packet and harmonic quanta are used to describe the physics of collapse for the first time.