Quasinormal modes and self-adjoint extensions of the Schroedinger operator

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

arXiv comment& pages, 1 Figure. Accepted for its publication in Physical Review D

References in corpus (11)

• Quasinormal modes of black holes and black branes
• Complex Extension of Quantum Mechanics
• Quasinormal modes of black holes: from astrophysics to string theory
• Self-adjoint extensions of operators and the teaching of quantum mechanics
• Pseudospectrum and black hole quasi-normal mode (in)stability
• Quasinormal modes of black holes and Borel summation
• Quasinormal modes in pure de sitter spacetimes
• Kermions: quantization of fermions on Kerr space-time
• Quasinormal modes for the scattering on a naked Reissner-Nordstrom singularity
• Quasinormal modes of generalized Pöschl-Teller potentials
• No asymptotically highly damped quasi-normal modes without horizons?

Cited by in corpus (7)

• Pseudospectrum and black hole quasi-normal mode (in)stability
• Quasinormal modes in the field of a dyon-like dilatonic black hole
• Quasinormal modes of dS and AdS Black Holes: Feedforward neural network method
• Scalar perturbations of black holes in Jackiw-Teitelboim gravity
• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
• Quasinormal modes and the analytical continuation of non-self-adjoint operators