Unified Theory of Wave-Particle Duality, the Schr\"odinger Equations, and Quantum Diffraction

Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Based on the unified theory of wave-particle duality, a straightforward derivation of the Schr"odinger equations is presented where previously no such derivation was considered to be possible. A new theory of quantum diffraction is subsequently developed.