On the pseudospectrum of the harmonic oscillator with imaginary cubic potential
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00235404" target="_blank" >RIV/68407700:21340/15:00235404 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/15:00450506
Result on the web
<a href="http://dx.doi.org/10.1007/s10773-015-2530-5" target="_blank" >http://dx.doi.org/10.1007/s10773-015-2530-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-015-2530-5" target="_blank" >10.1007/s10773-015-2530-5</a>
Alternative languages
Result language
angličtina
Original language name
On the pseudospectrum of the harmonic oscillator with imaginary cubic potential
Original language description
We study the Schrödinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and its spectrum isprovided and the importance of examining its pseudospectrum as well is emphasized. This is achieved by employing scaling techniques and treating the operator using semiclassical methods. The existence of pseudoeigenvalues very far from the spectrum is proven, and as a consequence, the spectrum of the operator is unstable with respect to small perturbations and the operator cannot be similar to a self-adjoint operator via a bounded and boundedly invertible transformation. It is shown that its eigenfunctions form a complete set in the Hilbert space of square-integrable functions; however, they do not form a Schauder basis.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
4142-4153
UT code for WoS article
000362889400027
EID of the result in the Scopus database
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