A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918419271516160 |
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| author | Ruck, Kevin |
| author_facet | Ruck, Kevin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_29201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces Ruck, Kevin Symplectic Geometry Mathematical Physics Quantum Physics 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. |
| title | A Floer Theoretic Approach to Energy Eigenstates on one Dimensional Configuration Spaces |
| topic | Symplectic Geometry Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2603.29201 |