Zusammenfassung
The Gamow vector description of resonances is compared with the S-matrix and
the Green function descriptions using the example of the square barrier
potential. By imposing different boundary conditions on the time independent
Schrodinger equation, we obtain either eigenvectors corresponding to real
eigenvalues and the physical spectrum or eigenvectors corresponding to complex
eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles
of the S matrix are the same as the poles of the Green function and are the
complex eigenvalues of the Schrodinger equation subject to a purely outgoing
boundary condition. The intrinsic time asymmetry of the purely outgoing
boundary condition is discussed. Finally, we show that the probability of
detecting the decay within a shell around the origin of the decaying state
follows an exponential law if the Gamow vector (resonance) contribution to this
probability is the only contribution that is taken into account.
Nutzer