The Schroedinger operator in Newtonian space-time
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2006
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| _version_ | 1866910654684725248 |
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| author | Grabowska, Katarzyna Grabowski, Janusz Urbański, Paweł |
| author_facet | Grabowska, Katarzyna Grabowski, Janusz Urbański, Paweł |
| contents | The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain one-dimensional complex vector bundle over space-time. This bundle, constructed from the data provided by all possible inertial observers, has no canonical trivialization, so these sections cannot be viewed as functions on the space-time. The presented framework is conceptually four-dimensional and does not involve any ad hoc or axiomatically introduced geometrical structures. It is based only on the traditional understanding of the Schroedinger operator in a given reference frame and it turns out to be strictly related to the frame-independent formulation of analytical Newtonian mechanics that makes a bridge between the classical and quantum theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_ph_0611044 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | The Schroedinger operator in Newtonian space-time Grabowska, Katarzyna Grabowski, Janusz Urbański, Paweł Mathematical Physics Differential Geometry 35J10; 70G45 The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain one-dimensional complex vector bundle over space-time. This bundle, constructed from the data provided by all possible inertial observers, has no canonical trivialization, so these sections cannot be viewed as functions on the space-time. The presented framework is conceptually four-dimensional and does not involve any ad hoc or axiomatically introduced geometrical structures. It is based only on the traditional understanding of the Schroedinger operator in a given reference frame and it turns out to be strictly related to the frame-independent formulation of analytical Newtonian mechanics that makes a bridge between the classical and quantum theory. |
| title | The Schroedinger operator in Newtonian space-time |
| topic | Mathematical Physics Differential Geometry 35J10; 70G45 |
| url | https://arxiv.org/abs/math-ph/0611044 |