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arXiv:quant-ph/9705010 · Foundations of Physics

Jordan blocks and exponentially decaying higher-order Gamow states

A. Bohm, M. Loewe, P. Patuleanu, C. Püntmann

Published May 1, 1997• 0 citations
arXivHTMLPDF
DOI
10.1007/bf02550171

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Resonances and decaying states have been associated with first-order poles of the S-matrix and represented by exponentially decaying Gamow kets using the Rigged Hilbert Space formulation of quantum mechanics. In analogy, higher-order S- matrix poles, represented by a mixture of Gamow-Jordan vectors, are associated with higher-order decaying states. The exact Golden Rule for decaying states associated to a higher-order pole of the S-matrix is calculated. These higher-order decaying states operators also obey the exponential decay law, but they have a more complicated linewidth than the Breit-Wigner energy distribution. This linewidth depends on the interaction V. To test whether these higher-order decaying state operators represent possible physical states, we discuss their linewidth for various assumptions about the matrix elements of V.