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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a quantum model with non-isotropic two-dimensional oscillatorpotential but with additional quadratic interaction $x_1x_2$ with imaginarycoupling constant. It is shown, that for a specific connection between couplingconstant and oscillator frequences, the model {\it is not} amenable to aconventional separation of variables. The property of shape invariance allowsto find analytically all eigenfunctions and the spectrum is found to beequidistant. It is shown that the Hamiltonian is non-diagonalizable, and theresolution of the identity must include also the corresponding associatedfunctions. These functions are constructed explicitly, and their properties areinvestigated. The problem of $R-$separation of variables in two-dimensionalsystems is discussed.

Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction