The interplay of supersymmetry and PT symmetry in quantum mechanics: a case study for the Scarf II potential
Result description
Motivated by the duality of normalizable states and the presence of the quasiparity quantum number q = ń1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example, the PT invariant version of the Scarf II potential is presented, and it is shown that the `bosonic` Hamiltonian has two different `fermionic` SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q = -1. It is shown that the `fermionic` potentials cease to be PT invariant when the PT symmetry of the `bosonic` potential is spontaneously broken.
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
The interplay of supersymmetry and PT symmetry in quantum mechanics: a case study for the Scarf II potential
Original language description
Motivated by the duality of normalizable states and the presence of the quasiparity quantum number q = ń1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example, the PT invariant version of the Scarf II potential is presented, and it is shown that the `bosonic` Hamiltonian has two different `fermionic` SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q = -1. It is shown that the `fermionic` potentials cease to be PT invariant when the PT symmetry of the `bosonic` potential is spontaneously broken.
Czech name
Souhra supersymetrie a PT-symetrie v kvantové mechanice: potenciál Scarf II
Czech description
Souhra supersymetrie a PT-symetrie v kvantové mechanice: potenciál Scarf II
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
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2002
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 General Physics
ISSN
0305-4470
e-ISSN
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Volume of the periodical
35
Issue of the periodical within the volume
41
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
8793-8804
UT code for WoS article
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EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2002