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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

For real functions \Phi and \Psi that are integrable and compactly supported,we prove the norm resolvent convergence, as \epsilon\ goes to 0, of a familyS(\epsilon) of one-dimensional Schroedinger operators on the line of the form  S(\epsilon)= -D^2 + \alpha \epsilon^{-2} \Phi(x/\epsilon) + \beta\epsilon^{-1} \Psi(x/\epsilon).  The limit results are shape-dependent: without reference to the convergenceof potentials in the sense of distributions the limit operator S(0) exists andstrongly depends on the pair (\Phi,\Psi). We show that it is impossible toassign just one self-adjoint operator to the pseudo-Hamiltonian -D^2 + \alpha\delta'(x) + \beta \delta(x), which is a symbolic notation only for a widevariety of quantum systems with quite different properties.

Schroedinger operators with (\alpha\delta'+\beta \delta)-like potentials: norm resolvent convergence and solvable models