On the incompleteness of the classification of quadratically integrable Hamiltonian systems in the three-dimensional Euclidean space
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913462305685504 |
|---|---|
| author | Snobl, Libor |
| author_facet | Snobl, Libor |
| contents | We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation cannot separate in any orthogonal coordinate system. This demonstrates a loophole in the derivation of the list of quadratically integrable Hamiltonian systems in [Makarov et al., A systematic search for nonrelativistic systems with dynamical symmetries. Nuovo Cimento A Series 10, 52:1061-1084, 1967] where only separable systems were found, and the need for its revision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the incompleteness of the classification of quadratically integrable Hamiltonian systems in the three-dimensional Euclidean space Snobl, Libor Mathematical Physics 70H06 (Primary) 70H20 (Secondary) We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation cannot separate in any orthogonal coordinate system. This demonstrates a loophole in the derivation of the list of quadratically integrable Hamiltonian systems in [Makarov et al., A systematic search for nonrelativistic systems with dynamical symmetries. Nuovo Cimento A Series 10, 52:1061-1084, 1967] where only separable systems were found, and the need for its revision. |
| title | On the incompleteness of the classification of quadratically integrable Hamiltonian systems in the three-dimensional Euclidean space |
| topic | Mathematical Physics 70H06 (Primary) 70H20 (Secondary) |
| url | https://arxiv.org/abs/2408.04457 |