By the same authors

From the same journal

From the same journal

A q-Schrödinger equation based on a Hopf q-deformation of the Witt algebra

Research output: Contribution to journalArticle

Published copy (DOI)



Publication details

JournalJournal of Physics A: Mathematical and General
DatePublished - 2 Jul 1999
Issue number26
Number of pages11
Pages (from-to)4971-4981
Original languageEnglish


In an earlier paper a q-Schrödinger equation was obtained based on a particular quantization procedure, called Borel quantization, and a related q-deformation of the Witt algebra. This q-deformation is a deformation in the category of Lie algebras and hence the corresponding q-Witt algebra has a trivial Hopf algebra structure. In this paper, we extend the above algebra by the addition of a set of shift-type generators, which appear in the expression for the quantum mechanical position operator and hence lead to a new type of quantum kinematics. The latter gives rise to a new kind of evolution equation and it is shown that in the limit q → 1 a specific class of Schrödinger equations is obtained from it. This specification of a particular class is a new phenomenon, because in earlier references, where a different q -deformation has been implemented or no deformation has been used at all, such a class could not be determined uniquely. The extended algebra used here has a nontrivial Hopf structure. The appearance of the shift-type generator in the q-deformed picture hence leads to a selection of a particular type of dynamics and delivers in the limit q → 1 new information for the characterization of the corresponding dynamics in the undeformed situation.

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations