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

Resonance (quasinormal) states correspond to non-Hermitian solutions to theSchr\"odinger equation obeying outgoing boundary conditions which lead tocomplex energy eigenvalues and momenta. Following the normalization rule forresonance states obtained from the residue at a complex pole of the outgoingGreen's function to the problem, we propose a definition of expectation valuefor these states and use it to investigate the extent of validity of theHeisenberg uncertainty relations for potentials that vanish after a distance.We derive analytical expressions for the expectation values involving themomentum and the position for a given resonance state and find in modelcalculations that the Heisenberg uncertainty relations are satisfied for abroad range of potential parameters. A comparison of our approach with thatbased on the regularization method by Zel'dovich yields very similar resultsexcept for resonance energies very close to the energy threshold. Our workshows that the validity of the Heisenberg uncertainty relations may be extendedto the non-Hermitian resonance state solutions to the Schr\"odinger equation.

Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schr\"odinger equation