Rudnicki, Lukasz (2016). Nonlinear Schrodinger equation from generalized exact uncertainty principle. J. Phys. A-Math. Theor., 49 (37). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121
Full text not available from this repository.Abstract
Inspired by the generalized uncertainty principle, which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle approach by Hall and Reginatto (2002 J. Phys. A: Math. Gen. 35 3289), and obtain a (quasi) nonlinear Schrodinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or plane-wave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitationally induced minimal position uncertainty proportional to the Planck length. Quite surprisingly, our result successfully merges the core of classical physics with non-relativistic quantum mechanics in its extremal form. We predict that the commonly accepted phenomenon, namely a modification of a free-particle dispersion relation due to quantum gravity might not occur in reality.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-262266 | ||||||||
| DOI: | 10.1088/1751-8113/49/37/375301 | ||||||||
| Journal or Publication Title: | J. Phys. A-Math. Theor. | ||||||||
| Volume: | 49 | ||||||||
| Number: | 37 | ||||||||
| Date: | 2016 | ||||||||
| Publisher: | IOP PUBLISHING LTD | ||||||||
| Place of Publication: | BRISTOL | ||||||||
| ISSN: | 1751-8121 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/26226 |
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