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A class of deformations of the Schrdinger representation of the Heisenberg commutation relation and exact solution to a Heisenberg equation and a Schrdinger equation
| Title: | A class of deformations of the Schrdinger representation of the Heisenberg commutation relation and exact solution to a Heisenberg equation and a Schrdinger equation |
| Authors: | Arai, A. Browse this author | | Kawano, H. Browse this author |
| Issue Date: | 1-Jun-2000 |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 485 |
| Start Page: | 1 |
| End Page: | 22 |
| Abstract: | We consider a class of representations {(Hv, Fv )}v of the Heisenberg commutation relation (HvFv - FvHv = -i) which are deformations of the Schrodinger representation, where the index parameter V is in a class of realvalued C00-functions on R. The Schrodinger representation is given by the case V = l. We classify the representations in terms of properties of V and show that they are divided into three subclasses. All elements of one of these subclasses are unitarily equivalent to the Schrodinger representation. But the others contain no elements unitarily equivalent to the Schrodinger representation. In particular a subclass consists of representations in each of which Hv has no self-adjoint extension. Moreover, we obtain exact solutions to the Heisenberg equation and the Schrodinger equation associated with Hv. We show that, even in the case where Hv has no self-adjoint extension, exact solutions local in time can be constructed. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69235 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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