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arXiv · 2603.29201

A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces

Kevin Ruck
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Abstract

In this article we consider two classical problems in Quantum Mechanics, namely the 'particle on a ring' and the 'particle in a box' from the viewpoint of symplectic topology. Interpreting the solutions of the corresponding time independent Schr\"odinger equation as orbits in a suitably chosen time dependent Hamiltonian system allows us to investigate them using Floer theory. More precisely we extend the definition of Rabinowitz Floer homology to non-autonomous Hamiltonians on $\mathbb{R}^{2n}$ with its standard symplectic structure and show that compactness of the moduli space of J-holomorphic curves still holds. With this homology we are then able to prove existence results for energy $E$ eigenstates on the 'ring' or in the 'box' for a big range of exterior potentials.

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BibTeXRIS

Kevin Ruck. 2026-03-31. A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces. https://arxiv.org/abs/2603.29201

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