Identification of observables in quantum toboggans
Result description
Schroedinger equations for 'quantum toboggans' with real energies are given the generalized eigenvalue-problem form H psi = EW psi, where H not equal H-dagger and W not equal W-dagger not equal I. The consistent probabilistic interpretation of these models is provided. The new double-series formula for the necessary ad hoc metric Theta = Theta( H, W) is derived which defines the acceptable inner products in the physical Hilbert space of states. The formula degenerates to the usual single series in the non-tobogganic trivial-weight limit W -> I.
Keywords
non-Hermitian HamiltoniansPT-symmetric potentialsanharmonic-oscillators
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
Identification of observables in quantum toboggans
Original language description
Schroedinger equations for 'quantum toboggans' with real energies are given the generalized eigenvalue-problem form H psi = EW psi, where H not equal H-dagger and W not equal W-dagger not equal I. The consistent probabilistic interpretation of these models is provided. The new double-series formula for the necessary ad hoc metric Theta = Theta( H, W) is derived which defines the acceptable inner products in the physical Hilbert space of states. The formula degenerates to the usual single series in the non-tobogganic trivial-weight limit W -> I.
Czech name
Identifikace pozorovatelných v kvantových tobogánech
Czech description
Schroedingerovy rovnice pro "kvantové tobogány" s reálnými energiemi jsou napsány ve tvaru zobecněného problému vlastních hodnot. Je uvedena konsistentní pravděpodobnostní interpretace studovaných modelů.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
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
21
Country of publishing house
GB - UNITED KINGDOM
Number of pages
14
Pages from-to
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UT code for WoS article
000256387800018
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
BE - Theoretical physics
Year of implementation
2008