Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs

Symmetry Integrability and Geometry-Methods and Applications

article

Andrey V. Sokolov¹ 

[1] V.A. Fock Department of Theoretical Physics, Sankt-Petersburg State University

关键词: non-Hermitian quantum mechanics;    supersymmetry;    exceptional points;    resolution of identity;   

DOI  :  10.3842/SIGMA.2011.112

来源: National Academy of Science of Ukraine

【 摘 要 】

This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.

【 授权许可】

Unknown