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 zeros of the eigenfunctions of self-adjoint Sturm-Liouville eigenvalueproblems interlace. For these problems interlacing is crucial for completeness.For the complex Sturm-Liouville problem associated with the Schrodingerequation for a non-Hermitian PT-symmetric Hamiltonian, completeness andinterlacing of zeros have never been examined. This paper reports a numericalstudy of the Sturm-Liouville problems for three complex potentials, the large-Nlimit of a -(ix)^N potential, a quasi-exactly-solvable -x^4 potential, and anix^3 potential. In all cases the complex zeros of the eigenfunctions exhibit asimilar pattern of interlacing and it is conjectured that this pattern isuniversal. Understanding this pattern could provide insight into whether theeigenfunctions of complex Sturm-Liouville problems form a complete set.

Conjecture on the interlacing of zeros in complex Sturm–Liouville problems