Convergent Quantum Normal Forms, \mathcal P\mathcal T-symmetry and reality of the spectrum

2012/06/04 by Emanuela Caliceti, Caliceti, Emanuela, Sandro Graffi +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1206.0582

arxiv created 2012/06/04 · openalex publication_date 2012/06/04 · arxiv updated 2012/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A class of non-selfadjoint, \PT-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal form, whose convergence (uniform with respect to the Planck constant) is proved. Further consequences of the uniform convergence of the quantum normal form are the establishment of an exact quantization formula for the eigenvalues.

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