共查询到19条相似文献,搜索用时 109 毫秒
1.
Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 (p - P) (q - Q), (q - Q) 3 (p - P), and (p, q), which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of (p, q) are also derived, which helps us to put the operators into their - and - ordering, respectively. 相似文献
2.
In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1/πexp[±2i≤(q-Q)(p-P)], here denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P-Q ordering, Q-P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained. 相似文献
3.
A generalized Weyl—Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators 下载免费PDF全文
By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented. 相似文献
4.
Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators' Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Eresnel transformation kernel in classical optics. 相似文献
5.
According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. bf282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented. 相似文献
6.
Operators’s-parameterized ordering and its classical correspondence in quantum optics theory 下载免费PDF全文
In reference to the Weyl ordering xmpn→(1/2)mΣι=0m(ιm)Xm-ιPnXι , where X and P are coordinate and momentum operator, respectively, this paper examines operators’s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence ((1-s)/2)(n+m)/2Hm,n((2/(1-s))~(1/2)α,(2/(1-s))~(1/2)α)→a+man,and its complementary relation αnα*m→(-i)n+m((1-s)/2)(m+n)/2:Hm,n(i(2/(1-s))~(1/2)a+,i((2/(1-s))~(1/2)a):,where H m,n is the two-variable Hermite polynomial, a, a+ are bosonic annihilation and creation operators respectively, s is a complex parameter. The s’-ordered operator power-series expansion of s-ordered operator sa+mans in terms of the two-variable Hermite polynomial is also derived. Application of operators’s-ordering formula in studying displaced-squeezed chaotic field is discussed. 相似文献
7.
Normal ordering and antinormal ordering of the operator (fQ+gP)n and some of their applications 下载免费PDF全文
In this paper by virtue of the technique of integration within an ordered product (IWOP) of operators and the intermediate coordinate-momentum representation in quantum optics, we derive the normal ordering and antinormal ordering products of the operator (f Q + gP )n when n is an arbitrary integer. These products are very useful in calculating their matrix elements and expectation values and obtaining some useful mathematical formulae. Finally, the applications of some new identities are given. 相似文献
8.
FAN Hong-Yi 《理论物理通讯》2008,50(10):935-937
We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i(p-x)(q-y)f(p,q)≡G(x,y),which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators. 相似文献
9.
Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |q〉λ,v of linear combination of the coordinate and momentum operator, (λQ + vP), where λ,v are real numbers, and |q〉λv is complete, then the projector |q〉λ,vλ,v〈q| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing. 相似文献
10.
FANHong-Yi 《理论物理通讯》2003,40(4):409-414
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated. 相似文献
11.
FAN Hong-Yi 《理论物理通讯》2008,50(4):935-937
We propose a new two-fold integration transformation in p-q phase space
∫∫-∞∞(dp dq/π)e2i(p-x)(q-y)f(p,q)≡G( x,y),
which possesses some well-behaved transformation properties. We apply this
transformation to the Weyl ordering of operators, especially those Q-P
ordered and P-Q ordered operators. 相似文献
12.
13.
By using the Weyl ordering operator formula and the Weyl transformation rule, we derive Weyl ordering of the two-mode Fresnel operator, and then obtain its matrix element in the coordinate representation, which is the integral kernel of the generalized two-mode Fresnel transformation in classical optics. By means of the optical operator method, we obtain a decomposition of the two-mode Fresnel operator’s Weyl ordering and an operator identity. 相似文献
14.
Optical Operator Method Studied via Fresnel Operator Decomposition and Coherent State Representation
MA Shan-Jun HU Li-Yun FAN Hong-Yi 《理论物理通讯》2008,49(5):1295-1298
We find that the mapping from classical optical transformations to
the optical operator method can be realized by using the coherent state
representation and the technique of integration within an ordered product of
operators. The optical Fresnel operator derived in (Commun. Theor. Phys.
(Beijing, China) 38 (2002) 147) can unify those frequently used optical operators. Various
decompositions of Fresnel operator into the exponential canonical operators
are obtained. 相似文献
15.
By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”. 相似文献
16.
The development of technique of integration within an ordered product (IWOP) of operators extends the Newton-Leibniz integration rule, originally applying to permutable functions, to the non-commutative quantum mechanical operators composed of Dirac’s ket-bra, which enables us to obtain the images of directly mapping symplectic transformation in classical phase space parameterized by [A, B; C, D] into quantum mechanical operator through the coherent state representation, we call them the generalized Fresnel operators (GFO) since they correspond to Fresnel transforms in Fourier optics. Based on GFO we find the ABCD rule for Gaussian beam propagation in the context of quantum optics (both in one-mode and two-mode cases) whose classical correspondence is just the ABCD rule in matrix optics. The entangled state representation is used in discussing the two-mode case. 相似文献
17.
FAN Hong-Yi 《理论物理通讯》2008,50(5):1089-1092
We re-explain the Weyl quantization scheme by virtue of the technique of
integration within Weyl ordered product of operators, i.e., the Weyl
correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave. 相似文献
18.
Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F2+ρF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented. 相似文献
19.
介绍经典菲涅耳变换的量子力学对应,它是相干态在相空间中的代表点做辛运动所对应的量子菲涅耳算符. 相似文献