  Two theoretical methods of finding resonant states in open quantum systems,
namely the approach of the Siegert boundary condition and the Feshbach
formalism, are reviewed and shown to be algebraically equivalent to each other
for a simple model of the T-type quantum dot. It is stressed that the seemingly
Hermitian Hamiltonian of an open quantum system is implicitly non-Hermitian
outside the Hilbert space. The two theoretical approaches extract an explicitly
non-Hermitian effective Hamiltonian in a contracted space out of the seemingly
Hermitian (but implicitly non-Hermitian) full Hamiltonian in the
infinite-dimensional state space of an open quantum system.
