2002/01/31 by Rafael de la Madrid, R. de la Madrid, M. Gadella · 79 citations
Engineering · Physics and Astronomy · #Archaeology #Autonomous Vehicle Technology and Safety #Computer science #Geography #Pedestrian #nucl-th #quant-ph
paper · pdf · doi:10.1119/1.1466817
published in American Journal of Physics 70(6), 626-638 (American Institute of Physics) · 25 RevTex pages, 3 figures
openalex publication_date 2002/05/13 · arxiv created 2002/06/11 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Schrödinger 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 Schrödinger 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.