English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We address the problem of integrating operator equations concomitant with thedynamics of non autonomous quantum systems by taking advantage of the use oftime-dependent canonical transformations. In particular, we proceed to adiscussion in regard to basic examples of one-dimensional non-autonomousdynamical systems enjoying the property that their Hamiltonian can be mappedthrough a time-dependent linear canonical transformation into an autonomousform, up to a time-dependent multiplicative factor. The operator equations weprocess essentially reproduce at the quantum level the classical integrabilitycondition for these systems. Operator series form solutions in the Bender-Dunnebasis of pseudo-differential operators for one dimensional quantum system aresought for such equations. The derivation of generating functions for thecoefficients involved in the \emph{minimal} representation of the seriessolutions to the operator equations under consideration is particularized. Wealso provide explicit form of operators that implement arbitrary lineartransformations on the Bender-Dunne basis by expressing them in terms of theinitial Weyl ordered basis elements. We then remark that the matching of theminimal solutions obtained independently in the two basis, i.e. the basis priorand subsequent the action of canonical linear transformation, is perfectlyachieved by retaining only the lowest order contribution in the expression ofthe transformed Bender-Dunne basis elements.

Non-autonomous Hamiltonian quantum systems, operator equations and  representations of Bender-Dunne Weyl ordered basis under time-dependent  canonical transformations