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International Journal of Quantum Chemistry

Gamow dyads and expectation values

Manuel Gadella, Roberto Laura

Published Jan 1, 2001• 14 citations
Publisher

Abstract

We analyze the possibilities to define density operators for the Gamow vectors in order to extend this concept to the Liouville space. We shall study the properties of the dyadic products of Gamow vectors and see that there exist difficulties if we try to obtain a Gamow density in Liouville space by factorizing Gamow vectors. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 307–320, 2001

DOI
10.1002/1097-461x(2001)81:5<307::aid-qua1000>3.0.co;2-5

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We analyze the possibilities to define density operators for the Gamow vectors in order to extend this concept to the Liouville space. We shall study the properties of the dyadic products of Gamow vectors and see that there exist difficulties if we try to obtain a Gamow density in Liouville space by factorizing Gamow vectors. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 307–320, 2001
As was repeatedly seen in the last chapter, for computing most of the usual matrix elements only a few of the many coordinates of an N -particle wavefunction are used, where due to the symmetry properties it is irrelevant which ones. Density matrices are a tool to extract the relevant information out of such monstrous constructs as are N -particle wavefunctions. (For reviews, see [Erdahl and Smith, 1987, Coleman, 1963, McWeeny, 1960]; in the text below we try to keep the notation as canonical as possible.) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.