  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.
