Publication:
Quasinormal modes and self-adjoint extensions of the Schrodinger operator

Дата
2021
Авторы
Fabris, J. C.
Richarte, M. G.
Saa, A.
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Организационные подразделения
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Институт ядерной физики и технологий
Цель ИЯФиТ и стратегия развития - создание и развитие научно-образовательного центра мирового уровня в области ядерной физики и технологий, радиационного материаловедения, физики элементарных частиц, астрофизики и космофизики.
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Аннотация
We revisit here the analytical continuation approach usually employed to compute quasinormal modes (QNM) and frequencies of a given potential barrier V starting from the bounded states and respective eigenvalues of the Schrodinger operator associated with the potential well corresponding to the inverted potential -V. We consider an exactly soluble problem corresponding to a potential barrier of the Poschl-Teller type with a well defined and behaved QNM spectrum, but for which the associated Schrodinger operator H obtained by analytical continuation fails to be self-adjoint. Although H admits self-adjoint extensions, we show that the eigenstates corresponding to the analytically continued QNM do not belong to any self-adjoint extension domain and, consequently, they cannot be interpreted as authentic quantum mechanical bounded states. Our result challenges the practical use of the this type of method when H fails to be self-adjoint since, in such cases, we would not have in advance any reasonable criterion to choose the initial eigenstates of H which would correspond to the analytically continued QNM.
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Quasinormal modes and self-adjoint extensions of the Schrodinger operator / Fabris, JC, Richarte, MG, Saa, A // Physical Review D. - 2021. - 103. - № 4. - 10.1103/PhysRevD.103.045001
URI
https://www.doi.org/10.1103/PhysRevD.103.045001
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85100957318&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000613522500013
 https://openrepository.mephi.ru/handle/123456789/23660
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