Seminario. Alberto Saa (Universidad de Campinas, Sao Paolo, Brasil)

Seminario CAPA

"Quasinormal modes and self-adjoint extensions of the Schrodinger operator"

A. Saa
Universidad de Campinas, Sao Paolo, Brasil

It is rather common to compute the quasinormal modes (QNM) and their associate frequencies of a given potential barrier $V$ starting from the bounded states and respective eigenvalues of the Schroedinger operator $H$ associated with the potential well corresponding to the inverted potential $−V$. This is the so-called analytical continuation method introduced by Blome, Ferrari, and Mashhoon in the 80s. We will present an exactly soluble problem corresponding to a potential barrier of the Poschl-Teller type with a well-behaved QNM spectrum, but for which the associated Schroedinger operator 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 bound states. This example challenges the practical use of the analytical continuation method when the Schroedinger operator fails to be self-adjoint since, in such cases, we would not have in advance any reasonable criterion to choose the initial eigenstates that would correspond to the analytically continued QNM.

Dia jueves 24
Hora 12:10
Lugar Seminario de Atomica, Molecular y Nuclear