Pith. sign in

REVIEW 1 cited by

Quasinormal modes and self-adjoint extensions of the Schroedinger operator

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2010.10674 v2 pith:4EOJ4N3X submitted 2020-10-20 gr-qc hep-thmath-phmath.MPquant-ph

Quasinormal modes and self-adjoint extensions of the Schroedinger operator

classification gr-qc hep-thmath-phmath.MPquant-ph
keywords self-adjointpotentialcorrespondingoperatorschroedingeranalyticalanalyticallyassociated
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original abstract

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 Schroedinger 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 Schroedinger operator $\cal H$ obtained by analytical continuation fails to be self-adjoint. Although $\cal H$ 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 $\cal H$ fails to be self-adjoint since, in such cases, we would not have in advance any reasonable criterion to choose the initial eigenstates of $\cal H$ which would correspond to the analytically continued QNM.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Pseudospectrum and black hole quasi-normal mode (in)stability

    gr-qc 2020-04 unverdicted novelty 6.0

    Pseudospectrum of Schwarzschild QNMs shows stability of the fundamental mode to infrared perturbations respecting asymptotics and instability of overtones to ultraviolet high-frequency perturbations.