Classification of certain pairs of operators (P,Q) satisfying \([P,Q]=- iId\) (Q801523)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Classification of certain pairs of operators (P,Q) satisfying \([P,Q]=- iId\) |
scientific article; zbMATH DE number 3879567
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of certain pairs of operators (P,Q) satisfying \([P,Q]=- iId\) |
scientific article; zbMATH DE number 3879567 |
Statements
Classification of certain pairs of operators (P,Q) satisfying \([P,Q]=- iId\) (English)
0 references
1984
0 references
In a separable Hilbert space a certain class of operators (P,Q) satisfying the Born-Heisenberg commutation relation \([P,Q]=-i Id\) on a dense domain \(\Omega\) is investigated. This class is essentially defined by requiring Q bounded and self-adjoint, P symmetric and \(P\Omega \subset \Omega,\) \(Q\Omega \subset \Omega.\) We show that Q is absolutely continuous and that P can be thought of as a first order differential operator.
0 references
Born-Heisenberg commutation relation
0 references
absolutely continuous
0 references
first order differential operator
0 references
