Abstract
In the framework of the rigged Hilbert space, unstable quantum systems associated with first-order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher-order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the set of higher-order Gamow vectors which obeys the exponential decay law. We shall discuss to what extent the requirement of an exponential time evolution determines the form of the state operator for a quasistationary microphysical system associated with a higher-order pole of the S-matrix.
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Dedicated to Professor L. P. Horwitz on the occasion of his 65th birthday, October 14, 1995.
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Bohm, A., Loewe, M., Patuleanu, P. et al. Jordan blocks and exponentially decaying higher-order Gamow states. Found Phys 27, 613–624 (1997). https://doi.org/10.1007/BF02550171
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DOI: https://doi.org/10.1007/BF02550171