annihilation operator

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annihilation operator

[ə‚nī·ə′lā·shən ¦äp·ə‚rād·ər]
(quantum mechanics)
An operator which reduces the occupation number of a single state by unity; for example, an annihilation operator applied to a state of one particle yields the vacuum. Also known as destruction operator.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
where u ([beta]) = cosh [theta]([beta]) and v'([beta]) = sinh [theta]([beta]), with [a.sup.[dagger].sub.p] and [a.sub.p] being creation and annihilation operators, respectively.
where u([beta]) = cos [theta]([beta]) and v([beta]) = sin [theta]([beta]), with [c.sup.[dagger].sub.p] and [c.sub.p] being creation and annihilation operators, respectively.
This allows us to express the Hamiltonian in terms of certain special operators on the stochastic Fock space: the creation and annihilation operators. Our notation here follows that used in quantum physics, where the creation and annihilation operators are adjoints of each other.
The Wheeler-DeWitt (WDW) equation is a result of quantization of a geometry and matter (second quantization of gravity), in this paper we consider the third quantization of a solvable inflationary universe model, i.e., by analogy with the quantum field theory, it can be done the second quantization of the universe wave function [psi] expanding it on the creation and annihilation operators (third quantization) [1].
This is in analogy with the quantum field theory, where [[??].sub.i] and [[??].sup.[dagger].sub.i] are creation and annihilation operators. Thus, we expect that the vacuum state in a third quantized theory is unstable and creation of universes from the initial vacuum state takes place.
We assume that the creation and annihilation operators of universes obey the standard commutation relations
The creation and annihilation operators of the third order for H' are described by expressions [s.sub.+] = [b.sub.+][a.sub.+][b.sub.-], = [b.sub.+][a.sub.-][b.sub.-], where [a.sub.+] and [a.sub.-] are the creation and annihilation operators for [H.sub.2].
The paper is presented as follows: in Section 2, we review how one can generate integrals of motion for two-dimensional superintegrable system from the creation and annihilation operators. In Section 3, we consider a particular quantum system for applying the Mielniks and Marquette's method and obtain a superintegrable potential separable in Cartesian coordinates.
where the creation and annihilation operators (polynomial in momenta) [A.sub.+](x), [A.sub.-](x), [A.sub.+](y), and [A.sub.-](y) satisfy the following equations:
In order to simplify the exposition, let us assume that [X.sup.*.sub.p] = [X.sub.p] (in fact, it turns out [3, 4,13] that one can always choose the phases of the creation and annihilation operators in such a way that the mean values (15) are real).
In order to recover the quasi-particles description of the low temperature behaviour of the system, it is convenient to introduce new creation and annihilation operators. The corresponding procedure is composed of two steps:
one can introduce new creation and annihilation operators [a.sup.[??].sub.ps] and [a.sub.ps] according to

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