Results 1 - 10 of 9735
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[en] We derive suitable uncertainty relations for characteristics functions of phase and number of a single-mode field obtained from the Weyl form of commutation relations. Some contradictions between the product and sums of characteristic functions are noted. - Highlights: • Phase–number uncertainty relations derived from Weyl commutation relations. • Phase–number uncertainty relations that include correlation terms. • Phase–number uncertainty relations in complete parallel with position–momentum.
[en] In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anti-commutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of Bernoulli numbers in quantum-mechanical identities such as the Baker–Campbell–Hausdorff formula is emphasized and applications connected to ordering problems as well as to the Ehrenfest theorem are proposed. (paper)
[en] The Baker–Campbell–Hausdorff formula is a general result for the quantity , where X and Y are not necessarily commuting. For completely general commutation relations between X and Y, (the free Lie algebra), the general result is somewhat unwieldy. However in specific physics applications the commutator , while non-zero, might often be relatively simple, which sometimes leads to explicit closed form results. We consider the special case , and show that in this case the general result reduces to Furthermore we explicitly evaluate the symmetric function , demonstrating that and relate this to previously known results. For instance this result includes, but is considerably more general than, results obtained from either the Heisenberg commutator or the creation-destruction commutator . (paper)
[en] We study nonclassicality in the product of the probabilities of noncommuting observables. We show that within the quantum theory, nonclassical states can provide larger probability product than classical states, so that nonclassical states approach the nonfluctuating states of the classical theory more closely than classical states. This is particularized to relevant complementary observables such as conjugate quadratures, phase and number, quadrature and number, and orthogonal angular momentum components.
[en] This paper sheds light on non-commutativity in quantum theory as regards theoretical estimation. In it, we calculate the quantum Cramer-Rao-type bound for many cases, by use of a newly proposed powerful technique. We also discuss the use of collective measurement in statistical estimation. (author)