Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.
By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.
By introducing the two-mode entangled state representation 〈η｜ whose one mode is a fictitious one accompanying the system mode, this paper presents a new approach for deriving density operator for describing continuum photodetection process.
By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional （2D） Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.
The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.
As a natural and important extension of Fan＇s paper （Fan Hong-Yi 2010 Chin. Phys. B 19 040305） by employing the formula of operators＇ Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator A （#, ~） （in its entangled form） in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to （a1-a2） and （a1＋a2） can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai are bosonic creation and annihilation operators, respectively.
Dirac's ket-bra formalism is the language of quantum mechanics.We have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors in previous work.In this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite polynomials.This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way.
FAN HongYi1,YUAN HongChun1 & JIANG NianQuan2 1Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China
In reference to the Weyl ordering xmpn→ （1/2）m ∑l=0m （ml）Xm-lPnXl , 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-sα,/2/1-sα）→αman and its complementary relation anam→（-i）n＋m（1-s/2）（m＋n）/2：Hm,n（i√2/1-sa,i√2/1-sa）,where Hrn,n is the two-variable Hermite polynomial, a, at are bosonic annihilation and creation operators respectively, s is a complex parameter. The s＇-ordered operator power-series expansion of s-ordered operator atraan 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.
