Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions
A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system...
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| Format: | Article |
| Language: | English English |
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Institute of Physics Publishing (UK)
2014
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| Online Access: | http://irep.iium.edu.my/39452/ http://irep.iium.edu.my/39452/1/39452_Quadratic%20plus%20linear%20operators.pdf http://irep.iium.edu.my/39452/2/39452_Quadratic%20plus%20linear%20operators_SCOPUS.pdf |
| _version_ | 1848781786984742912 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system. |
| first_indexed | 2025-11-14T15:55:06Z |
| format | Article |
| id | iium-39452 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T15:55:06Z |
| publishDate | 2014 |
| publisher | Institute of Physics Publishing (UK) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-394522017-09-20T08:42:26Z http://irep.iium.edu.my/39452/ Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions Saburov, Mansoor QA Mathematics A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system. Institute of Physics Publishing (UK) 2014-11-20 Article PeerReviewed application/pdf en http://irep.iium.edu.my/39452/1/39452_Quadratic%20plus%20linear%20operators.pdf application/pdf en http://irep.iium.edu.my/39452/2/39452_Quadratic%20plus%20linear%20operators_SCOPUS.pdf Saburov, Mansoor (2014) Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions. Journal of Physics: Conference Series, 553 (1). pp. 1-11. ISSN 1742-6588 E-ISSN 1742-6596 http://iopscience.iop.org/article/10.1088/1742-6596/553/1/012003 10.1088/1742-6596/553/1/012003 |
| spellingShingle | QA Mathematics Saburov, Mansoor Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title | Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title_full | Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title_fullStr | Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title_full_unstemmed | Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title_short | Quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| title_sort | quadratic plus linear operators which preserve pure states of quantum systems: small dimensions |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/39452/ http://irep.iium.edu.my/39452/ http://irep.iium.edu.my/39452/ http://irep.iium.edu.my/39452/1/39452_Quadratic%20plus%20linear%20operators.pdf http://irep.iium.edu.my/39452/2/39452_Quadratic%20plus%20linear%20operators_SCOPUS.pdf |