The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets

Abstract

The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting into a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.

arXiv comment32 pages, 3 figures

References in corpus (3)

• Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics
• The Rigged Hilbert Space of the Free Hamiltonian
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

Cited by in corpus (5)

• The rigged Hilbert space approach to the Gamow states
• The resonance amplitude associated with the Gamow states
• On the inconsistency of the Bohm-Gadella theory with quantum mechanics
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''