SMATRIX.bib

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@MISC{delaMadrid2002pedestrian,
  AUTHOR = {R. de la Madrid, M. Gadella},
  TITLE = {A Pedestrian Introduction to Gamow Vectors},
  YEAR = {2002},
  URL = {http://fr.arxiv.org/abs/quant-ph/0201091},
  PS = {/sci_docs/physics/papers/arxiv/delaMadrid2002pedestrian.ps.gz},
  ROPSECTIONS = {SMATRIX QUANTPHYS},
  ABSTRACT = { The Gamow vector description of resonances is
                  compared with the S-matrix and the Green function
                  descriptions using the example of the square barrier
                  and similar potentials. By imposing different
                  boundary conditions on the time independent
                  Schrodinger equation, we get either eigenvectors
                  corresponding to real eigenvalues (Dirac kets) and
                  the real ``physical'' spectrum or we get
                  eigenvectors corresponding to complex eigenvalues
                  (Gamow vectors) and the resonance spectrum. We will
                  show that the poles of the S-matrix are the same as
                  the poles of the Green function and as the complex
                  eigenvalues of the Schrodinger equation subject to a
                  purely outgoing boundary condition. We also obtain
                  the basis vector expansion generated by the Gamow
                  vectors. The time asymmetry built into the purely
                  outgoing boundary condition will be revealed. It
                  will be also shown that the probability to detect
                  the decay within a shell around the origin of the
                  decaying state follows the exponential law if the
                  Gamow vector (resonance) contribution to this
                  probability is the only contribution that is taken
                  into account. }
}

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