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

• URL: http://arxiv.org/abs/2603.29201v1
• Date: Tue, 31 Mar 2026 03:12:03 GMT
• Title: A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces
• Abstract summary: We consider two classical problems in Quantum Mechanics, namely the 'particle on a ring' and the 'particle in a box'<n>We extend the definition of Rabinowitz Floer homology to non-autonomous Hamiltonians on $mathbbR2n$ with its standard symplectic structure.
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• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 Schrödinger 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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