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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The existence of potentials for relativistic Schrodinger operators allowingeigenvalues embedded in the essential spectrum is a long-standing open problem.We construct Neumann-Wigner type potentials for the massive relativisticSchrodinger operator in one and three dimensions for which an embeddedeigenvalue exists. We show that in the non-relativistic limit these potentialsconverge to the classical Neumann-Wigner and Moses-Tuan potentials,respectively. For the massless operator in one dimension we construct twofamilies of potentials, different by the parities of the (generalized)eigenfunctions, for which an eigenvalue equal to zero or a zero-resonanceexists, dependent on the rate of decay of the corresponding eigenfunctions. Weobtain explicit formulae and observe unusual decay behaviours due to thenon-locality of the operator.

Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators