共查询到20条相似文献,搜索用时 31 毫秒
1.
FAN Hong-Yi FU Liang 《理论物理通讯》2006,46(2):213-216
We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula. 相似文献
2.
FAN Hong-yi 《理论物理通讯》1989,12(2):219-227
In this paper, the completeness relations of the fundamental representations in quantum mechanics, together with the "integration within orderd product" technique are exploited to derive normally ordered and antinormally ordered expansions of some exponential operators in Hilbert space. Applications of the normally ordered exponential operators to evaluating Feynman matrix element in coherent state representation are given, which seems to be a new approach. 相似文献
3.
Hong-Yi FAN 《理论物理通讯》1992,17(3):355-360
Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product technique, and the mapping is maniferrtly apparent in the derivation. New generalixed coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed. 相似文献
4.
The paper is devoted to algebraic structures connected with the logic of quantum mechanics. Since every (generalized) effect algebra with an order determining set of (generalized) states can be represented by means of an abelian partially ordered group and events in quantum mechanics can be described by positive operators in a suitable Hilbert space, we are focused in a representation of partially ordered abelian groups by means of sets of suitable linear operators. We show that there is a set of points separating ?-maps on a given partially ordered abelian group G if and only if there is an injective non-trivial homomorphism of G to the symmetric operators on a dense set in a complex Hilbert space $\mathcal{H}$ which is equivalent to an existence of an injective non-trivial homomorphism of G into a certain power of ?. A similar characterization is derived for an order determining set of ?-maps and symmetric operators on a dense set in a complex Hilbert space $\mathcal{H}$ . We also characterize effect algebras with an order determining set of states as interval operator effect algebras in groups of self-adjoint bounded linear operators. 相似文献
5.
Hausdorff momentum problem and its relations to spectral theorem for bounded Hilbert space operators are treated. A generalization for some ordered algebras is shown, where projections are replaced by idempotents. 相似文献
6.
FAN Hong-Yi HU Shan 《理论物理通讯》2006,46(7)
We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too. 相似文献
7.
FAN Hong-Yi HU Shan 《理论物理通讯》2006,46(1):55-57
We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too. 相似文献
8.
FAN Hong-Yi 《理论物理通讯》2004,41(2):205-208
Based on the technique of integral within a Weyl ordered product of
operators, we present applications of the Weyl ordered two-mode Wigner
operator for quantum mechanical entangled system, e.g., we derive the
complex Wigner transform and its relation to the complex fractional Fourier
transform, as well as the entangled Radon transform. 相似文献
9.
By virtue of the method of integration within ordered product(IWOP)of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform(WFrST)operator.The way we successfully combine them to realize the integration transform kernel of WFr ST is making full use of the completeness relation of Dirac’s ket–bra representation.The WFr ST can play role in analyzing and recognizing quantum states,for instance,we apply this new transform to identify the vacuum state,the single-particle state,and their superposition state. 相似文献
10.
Gerd Niestegge 《Foundations of Physics》2014,44(11):1216-1229
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lüders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate—the non-existence of third-order interference [third-order interference and its impossibility in quantum mechanics were discovered by Sorkin (Mod Phys Lett A 9:3119–3127, 1994)]. This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed. 相似文献
11.
Let H be a separable infinite-dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on H without the assumption on continuity are also presented. 相似文献
12.
《中国物理快报》2016,(11)
Based on Dirac's representation theory and the technique of integration within an ordered product of operators,we put forward the joint wavelet-fractional Fourier transform in the context of quantum mechanics.Its corresponding transformation operator is found and the normally ordered form is deduced.This kind of transformation may be applied to analyzing and identifying quantum states. 相似文献
13.
14.
Jan Paseka 《International Journal of Theoretical Physics》2011,50(4):1198-1205
We show that an η
+-pseudo-Hermitian operator for some metric operator η
+ of a quantum system described by a Hilbert space H{\mathcal{H}} yields an isomorphism between the partially ordered commutative group of linear maps on H{\mathcal{H}} and the partially ordered commutative group of linear maps on Hr+{\mathcal{H}}_{\rho_{+}}. The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces H{\mathcal{H}} and Hr+{\mathcal{H}}_{\rho_{+}}. Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide. 相似文献
15.
We introduce the bipartite entangled states to present a quantum mechanical version of complex wavelet transform. Using the technique of integral within an ordered product of operators we show that the complex wavelet transform can be studied in terms of various quantum state vectors in two-mode Fock space. In this way the creterion for mother wavelet can be examined quantum-mechanically and therefore more deeply. 相似文献
16.
Using the technique of integral within an ordered product (IWOP) of
operators we show that the wavelet transform can be recasted to a matrix
element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum
mechanics. In this way many quantum optical states' wavelet transform can be
easily derived. 相似文献
17.
Anatolij Dvurečenskij 《International Journal of Theoretical Physics》2016,55(11):4896-4912
M.P. Olson, Proc. Am. Math. Soc. 28, 537–544 (1971) showed that the system of effect operators of the Hilbert space can be ordered by the so-called spectral order such that the system of effect operators is a complete lattice. Using his ideas, we introduce a partial order, called the Olson order, on the set of bounded observables of a complete lattice effect algebra. We show that the set of bounded observables is a Dedekind complete lattice. 相似文献
18.
Gianpiero Cattaneo 《International Journal of Theoretical Physics》1992,31(9):1573-1597
The partial ordered structure which plays for unsharp quantum mechanics the same role of orthomodular lattices for ordinary quantum mechanics is introduced. Differently from the unsharp case, in which one can identify quantum propositions (i.e., Hilbert space subspaces) with yes-no devices (i.e., orthogonal projections) they are tested by, in the unsharp case this identification is broken down: every quantum generalized proposition (i.e., pair of mutually orthogonal subspaces) is tested by many different yes-no devices (i.e., Hilbert space effects). The set of all quantum effects has a structure of Brouwer-Zadeh poset, canonically embeddable in a (minimal) Brouwer-Zadeh lattice, whereas the set of all quantum generalized propositions has a structure of Brouwer-Zadeh complete lattice.A Brouwer-Zadeh poset is defined as a partially ordered structure equipped with two nonusual orthocomplementations: a regular degenerate (Zadeh or fuzzy-like) one and a weak (Brouwer or intuitionistic-like) one linked by an interconnection rule. Using these two orthocomplementations it is possible to introduce the two modal-like operators of necessity and possibility. 相似文献
19.
Volker Schomerus 《Communications in Mathematical Physics》1995,169(1):193-236
It has been discussed earlier that (weak quasi-) quantum groups allow for a conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses the reconstruction of quantum symmetries and algebras of field operators. For every algebraA of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field operators are obtained which act on a positive definite Hilbert space of states and transform covariantly under the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation relations, these fields are demonstrated to obey a local braid relation. 相似文献
20.
F. Debacker-Mathot 《Communications in Mathematical Physics》1980,71(1):47-58
We give a meaning to the direct integral decomposition of unbounded operators and Op*-algebras on a metrizable dense domain of a Hilbert space, by considering them as bounded operators between several other Hilbert spaces. 相似文献