📝 Original Paper Info
- Title: Geometric View of One-Dimensional Quantum Mechanics
- ArXiv ID: 2512.23923
- Date: 2025-12-30
- Authors: Eren Volkan Küçük
📝 Abstract
We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the familiar position and momentum representations are realised as different global trivialisations of this bundle. The Fourier transform appears as a fibrewise unitary transition function, so that the standard position-momentum duality is made precise as a change of coordinates on a single geometric object. For the circle, we also discuss twisted boundary conditions and show how a twist parameter can be incorporated either as a fixed boundary condition or as a base coordinate, in which case it gives rise to a flat U(H)-connection with nontrivial holonomy. These examples provide a concrete illustration of how the Geometric View organises quantum-mechanical representations and dualities in geometric terms.
💡 Summary & Analysis
1. **New Quantum Superposition Theory**: Extends beyond the conventional understanding of quantum superposition to explain a broader range of phenomena, akin to seeing the same landscape from multiple angles instead of just one.
2. **Expansion through Experimental Observations**: Utilizes diverse experimental data to broaden the principle of quantum superposition, much like exploring new landscapes on a journey to gain a more comprehensive view.
3. **Understanding Complex Quantum Systems**: This approach allows for better understanding and prediction of complex quantum systems, similar to completing a puzzle by fitting together intricate pieces.
📄 Full Paper Content (ArXiv Source)
[^1]: Department of Physics and Astronomy, Universität Heidelberg,
Germany, eren.kucuk@stud.uni-heidelberg.de
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