On pairs of difference operators satisfying [D, X]=Id
- 1 January 1998
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 39 (1) , 545-568
- https://doi.org/10.1063/1.532322
Abstract
Dedicated to the memory of Gerda Dorfmeister. Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider D and X to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of [D, X]=Id.Keywords
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