 02259 R de la Madrid, M Gadella
 A Pedestrian Introduction to Gamow Vectors
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Jun 11, 02

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Abstract. The Gamow vector description of resonances is compared with the
Smatrix 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.
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