In:
Journal of Mathematical Physics, AIP Publishing, Vol. 30, No. 9 ( 1989-09-01), p. 2083-2089
Abstract:
Bounds are proved for the C*-algebraic transition probability PA(ω,ν) between the abstract ground state ν with respect to a symmetric subspace N of a unital C* algebra A and a state ω with the restriction ω‖N=σ‖N to N for an arbitrarily given, but fixed state σ. A is assumed to be the unital C*-algebra generated by N. The results are specified in the case where A is a subalgebra of a vN algebra in standard form and N is dimensionally finite. Under these assumptions, the relationships of the algebraic transition probability to the notion of the (square of the) overlap integral known in quantum physics are clearly established. The general results are used to treat the standard problem of finding upper and lower bounds to the overlap in a quantum mechanical context. The best bounds are found and their properties discussed.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
1989
detail.hit.zdb_id:
1472481-9
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