The rigged Hilbert space approach to the Gamow states

Abstract

We use the resonances of the spherical shell potential to present a thorough description of the Gamow (quasinormal) states within the rigged Hilbert space. It will be concluded that the natural setting for the Gamow states is a rigged Hilbert space whose test functions fall off at infinity faster than Gaussians.

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Cited by in corpus (13)

• Eigenvector continuation for emulating and extrapolating two-body resonances
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• The decay widths, the decay constants, and the branching fractions of a resonant state
• Bound states of dipolar molecules studied with the Berggren expansion method
• Perturbation theory of optical resonances of deformed dielectric spheres
• Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation
• Unified exact WKB framework for resonance -- Zel'dovich/complex-scaling regularization and rigged Hilbert space
• Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method
• Unearthing wave-function renormalization effects in the time evolution of a Bose-Einstein condensate
• Characteristic influence of exceptional points in quantum dynamics