Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 043, 14 pages      arXiv:0904.1372      https://doi.org/10.3842/SIGMA.2009.043
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries

Rafael de la Madrid
Department of Physics, The Ohio State University at Newark, Newark, OH 43055 USA

Received November 07, 2008, in final form March 30, 2009; Published online April 08, 2009

Abstract
We review the way to analytically continue the Lippmann-Schwinger bras and kets into the complex plane. We will see that a naive analytic continuation leads to nonsensical results in resonance theory, and we will explain how the non-obvious but correct analytical continuation is done. We will see that the physical basis for the non-obvious but correct analytic continuation lies in the invariance of the Hamiltonian under anti-unitary symmetries such as time reversal or PT.

Key words: Lippmann-Schwinger equation; resonances; Gamow states; resonant expansions; time reversal; PT symmetry.

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