Eigenfunction expansions and Lippmann-Schwinger formulas

DOI10.1016/S0034-4877(12)60008-1zbMath1250.81120OpenAlexW2153774168MaRDI QIDQ442060

Piotr Kielanowski, Manuel Gadella

Publication date: 9 August 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(12)60008-1

zbMATH Keywords

eigenfunction expansionsrigged Hilbert spaceGamow vectorsLippmann-Schwinger equations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) (2)-body potential quantum scattering theory (81U05) Resonance in context of PDEs (35B34) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Cites Work

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• The analytic continuation of the Lippmann-Schwinger eigenfunctions, and antiunitary symmetries
• Complex dynamical variables for multiparticle systems with analytic interactions. I
• Dirac kets, Gamov vectors and Gel'fand triplets. The rigged Hilbert space and quantum mechanics. Lectures in mathematical physics at the University of Texas at Austin
• Derivation of Gamow vectors for resonances in cut-off potentials
• Vector states for single an multiple-pole resonances
• Extending the stationary quantum mechanics of being to a nonstationary quantum theory of becoming and decaying
• Resonances and time reversal operator in rigged Hilbert spaces
• The decay-scattering system
• Causality and dispersion relations for fixed momentum transfer
• The Lippmann-Schwinger equations in the rigged Hilbert space
• Time asymmetric quantum theory – III. Decaying states and the causal Poincaré semigroup

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