Geometric Approach to Quantum Mechanics

This paper offers a geometric perspective on one-dimensional quantum mechanics, using the framework of De Haro's Geometric View of Theories. It clarifies the relationship between position and momentum representations as different trivializations of a Hilbert bundle, and the Fourier transform as a transition function. The analysis extends to the circle, incorporating twisted boundary conditions and connections. This approach provides a novel way to understand quantum mechanical representations and dualities.