Jordan Blocks and Exponentially Decaying Higher Order Gamow States

Details Jordan Blocks and Exponentially Decaying Higher Order Gamow States Jordan Blocks and Exponentially Decaying Higher Order Gamow States

1997-05-07

arxiv.org/abs/quant-ph/9705010v1

Physics

Quantum Physics

Dedicated to L. P. Horwitz on the occasion of his 65th birthday; 11 pages, no figures, uses subeqnarray.sty; to appear in Foun

Scientific paper

10.1007/BF02550171

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 extend 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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