Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912996197924864 |
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| author | Acharya, Amit |
| author_facet | Acharya, Amit |
| contents | The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schrödinger equation, with the expected limiting form when the associated classical force system involves conservative forces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity Acharya, Amit Mathematical Physics Classical Physics Quantum Physics The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schrödinger equation, with the expected limiting form when the associated classical force system involves conservative forces. |
| title | Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity |
| topic | Mathematical Physics Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.21281 |