Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Hunan University of Science and Engineering

Teaching discussion on the integration technique of ordered product of operators and its applications

Xia Li-xin

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In quantum mechanics,we introduce the integration technique of ordered product of Boson operators.Where we present the properties of ordered product of operators and its applications,integration technique,and some applied examples.Specially,we present the teaching discussion on integration technique of ordered product of operators and its applications.

Related papers

On the Weyl Ordering Operation

Hong-Yi Fan, Hai-Guang Weng

A Weyl ordering product operation (with its representative symbol) is introduced. On the basis of the operation, a technique of integration within a Weyl ordered product is put forward. Application of the technique to the coherent state representation leads us to derive the Weyl ordered forms of some important operators in quantum mechanics, which can be rigorously checked by the relation between our Weyl ordering product operation and the Weyl correspondence rule.

Communications in Theoretical Physics•Sep 1, 1992•0 citations

Normally Ordered Operator Fredholm Equation and Its Applications in Quantum Mechanics

Fan Hong‐Yi, Fan Yue

By virtue of the technique of integration within an ordered product of operators we construct the normally ordered operator fiedholm equation. We use it to derive some new operator formulas. For Weyl correspondence, operator fiedholm equation can also be constructed. Some applications of the operator Fkedholm equation are given.

Communications in Theoretical Physics•Jul 30, 2000•11 citations

ENTANGLED STATES, SQUEEZED STATES GAINED VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD AND THEIR APPLICATIONS

Hong-Yi Fan

Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.

International Journal of Modern Physics B•Apr 30, 2004•100 citations

Weyl ordering quantum mechanical operators by virtue of the IWWP technique

Fan Hong-Yi

The properties of Weyl ordered products of operators are investigated and the technique of integration within Weyl ordered product (IWWP) is introduced. The overcompleteness relation of the coherent state is then recast into Weyl ordered form. In so doing, a new approach for Weyl ordering quantum mechanical operators is presented.

Journal of Physics A Mathematical and General•Jun 7, 1992•82 citations

About integration within ordered products in quantum optics

Alfred Wünsche

The fundamentals of Fan's method of integration within ordered products are investigated and it is shown that it is a reliable calculation method in quantum optics. Differentiation within ordered products is included into the considerations. The integrations are, in applications to single boson modes, mostly one-dimensional or two-dimensional integrations over phase-space variables. We examine some examples of integration within ordered products and compare them with calculations of results by other methods such as Lie group methods. A new representation of the main class of quasiprobabilities including the Wigner and the Husimi-Kano quasiprobability is derived by the method. Different representations of squeezing operators are related by the method and discussed. As a further new result, the position and momentum representation of the general unitary squeezing operators are derived and specialized to cases with squeezing in the direction of the coordinate axes which were earlier dealt with by the method under consideration.

Journal of Optics B Quantum and Semiclassical Optics•Jan 1, 1999•210 citations

A new kind of special function and its application

范洪义, M LONG, 吴泽 +1 more

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.

中国物理B：英文版•Jan 1, 2015•0 citations
In quantum mechanics,we introduce the integration technique of ordered product of Boson operators.Where we present the properties of ordered product of operators and its applications,integration technique,and some applied examples.Specially,we present the teaching discussion on integration technique of ordered product of operators and its applications.
Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.
The fundamentals of Fan's method of integration within ordered products are investigated and it is shown that it is a reliable calculation method in quantum optics. Differentiation within ordered products is included into the considerations. The integrations are, in applications to single boson modes, mostly one-dimensional or two-dimensional integrations over phase-space variables. We examine some examples of integration within ordered products and compare them with calculations of results by other methods such as Lie group methods. A new representation of the main class of quasiprobabilities including the Wigner and the Husimi-Kano quasiprobability is derived by the method. Different representations of squeezing operators are related by the method and discussed. As a further new result, the position and momentum representation of the general unitary squeezing operators are derived and specialized to cases with squeezing in the direction of the coordinate axes which were earlier dealt with by the method under consideration.