Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
Result description
n a previous paper [1] we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with a real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this paper we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction-based on a backward use of the spectral theorem for self-adjoint operators-provides new insights into the nature of the model.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
Original language description
n a previous paper [1] we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with a real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this paper we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction-based on a backward use of the spectral theorem for self-adjoint operators-provides new insights into the nature of the model.
Czech name
Výpočet metriky v Hilbertově prostoru PT-symetrického modelu pomocí spektrálního terorému
Czech description
V předchozím článku (J.Phys.A39-2006, 10143-10152) jsme zavedli jednoduchý PT-symetrický nehermitovský hamiltonián s reálným spektrem a odvodili Formulku pro metrický operátor v uzavřeném tvaru.V tomto článku navrhujeme alternativní metodu pro výpočet metriky, jež je založena na obráceném užití spektrálního teorému.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A-Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
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Volume of the periodical
41
Issue of the periodical within the volume
24
Country of publishing house
GB - UNITED KINGDOM
Number of pages
4
Pages from-to
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UT code for WoS article
000256388200013
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2008