TY - JOUR

T1 - Sz.-Nagy-Foias theory and Lax-Phillips type semigroups in the description of quantum mechanical resonances

AU - Strauss, Y.

N1 - Funding Information:
The author wishes to thank L.P. Horwitz and Paul A. Fuhrmann for useful discussions. Research supported by The Israel Science Foundation (Grant No. 188/02) and the Edmund Landau Center for Research in Mathematical Analysis and Related areas, sponsored by the Minerva Foundation (Germany).

PY - 2005/3/1

Y1 - 2005/3/1

N2 - A quantum mechanical version of the Lax-Phillips scattering theory was recently developed. This theory is a natural framework for the description of quantum unstable systems. However, since the spectrum of the generator of evolution in this theory is unbounded from below, the existing framework does not apply to a large class of quantum mechanical scattering problems. It is shown in this work that the fundamental mathematical structure underlying the Lax-Phillips theory, i.e., the Sz.-Nagy-Foias theory of contraction operators on Hubert space, can be used for the construction of a formalism in which models associated with a semibounded spectrum may be accomodated.

AB - A quantum mechanical version of the Lax-Phillips scattering theory was recently developed. This theory is a natural framework for the description of quantum unstable systems. However, since the spectrum of the generator of evolution in this theory is unbounded from below, the existing framework does not apply to a large class of quantum mechanical scattering problems. It is shown in this work that the fundamental mathematical structure underlying the Lax-Phillips theory, i.e., the Sz.-Nagy-Foias theory of contraction operators on Hubert space, can be used for the construction of a formalism in which models associated with a semibounded spectrum may be accomodated.

UR - http://www.scopus.com/inward/record.url?scp=17744365991&partnerID=8YFLogxK

U2 - 10.1063/1.1849831

DO - 10.1063/1.1849831

M3 - Article

AN - SCOPUS:17744365991

SN - 0022-2488

VL - 46

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

M1 - 032104

ER -