Resonance expansions in quantum mechanics

Abstract

The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.

10 pages and 1 figure; presented at the Istanbul workshop on pseudo-Hermitian Hamiltonians

References in corpus (5)

• A Pedestrian Introduction to Gamow Vectors
• Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix
• Siegert pseudostates: completeness and time evolution
• Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics
• Transient response of a quantum wave to an instantaneous potential step switching

Cited by in corpus (19)

• Some properties of the resonant state in quantum mechanics and its computation
• Time-reversal symmetric resolution of unity without background integrals in open quantum systems
• Resonant Spectrum Analysis of the Conductance of Open Quantum System and Three Types of Fano Parameter
• Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states
• The rigged Hilbert space approach to the Gamow states
• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Probabilistic Interpretation of Resonant States
• Flow of S-matrix poles for elementary quantum potentials
• Nonexponential tunneling decay of a single ultracold atom
• The resonance amplitude associated with the Gamow states
• Inner products of resonance solutions in 1-D quantum barriers
• Towards scalable bound-to-resonance extrapolations for few- and many-body systems
• Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Underlying non-Hermitian character of the Born rule in open quantum systems
• Convergence and completeness for square-well Stark resonant state expansions
• Constructing a partially transparent computational boundary for UPPE using leaky modes