A Geometric Projective Formulation of the Double-Slit Experiment

The aim of the present lecture note is not to propose an alternative formulation of quantum mechanics, but to emphasize that several apparently distinct descriptions of the double-slit experiment may be understood as complementary consequences of a single geometric projection onto the transmission subspace defined by the apertures. Modeling the double slit as a projection onto the two-dimensional transmission subspace spanned by the localized slit modes provides a common mathematical framework for the wave-based, particle-based and information-theoretic descriptions of interference. The formalism starts from an arbitrary incident localized wave packet and naturally reproduces Duane's momentum-selection law, which emerges directly from the geometric transmission condition rather than being introduced as an independent postulate.