HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

A class of deformations of the Schrdinger representation of the Heisenberg commutation relation and exact solution to a Heisenberg equation and a Schrdinger equation

Files in This Item:
pre485.pdf878.56 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83631

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

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University