Geometric Approach to Quantum Mechanics
Published:Dec 30, 2025 00:48
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Applies the Geometric View of Theories to one-dimensional quantum systems.
- •Clarifies the relationship between position and momentum representations.
- •Provides a geometric interpretation of the Fourier transform.
- •Discusses twisted boundary conditions and their geometric implications.
Reference
“The paper demonstrates how the Geometric View organizes quantum-mechanical representations and dualities in geometric terms.”