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General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

Fan Hong‐Yi, Shan Hu

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.

Communications in Theoretical PhysicsJul 1, 20060 citations

The IWOP Method of Normally Ordering Multimode Exponential Operators

Luo-Yu Feng

This paper states that the technique of integration within ordered product (IWOP) provides us with a generally effective approach to normally ordering multimode exponential operators. In fact, all the operators listed in Ref. [5] can be normally ordered by virtue of IWOP, in contrast to the comment of Ref. [5].

Communications in Theoretical PhysicsDec 1, 19930 citations

Normally ordering some multimode exponential operators by virtue of the IWOP technique

Fan Hong-Yi

The author shows that the technique of integration within an ordered product (IWOP) provides one with a very simple approach to deriving the normal product form of some multimode exponential operators, which greatly simplifies the calculations of normalising some state vectors in Hilbert space.

Journal of Physics A Mathematical and GeneralMay 21, 199024 citations

New Approach for Finding the Phase Shift Operator via the IWOP Technique

Gang Ren, Shuangxi Zhang

We present a new approach for finding the explicit expression of the unitary phase operator by the technique of integration within an ordered product (IWOP) of an operator. An adaptive estimation scheme to measure the phase shift angle in the two-mode case is also given.

Chinese Journal of PhysicsApr 1, 20100 citations

The Coherent-State Method of Normally Ordering Multimode Exponential Operators

Gong Ren-shan

This work shows that the coherent-state method provides us a very simple approach to normally ordering multimode exponential operators, many of which can't be normally ordered simply by the technique of integration within an ordered product (IWOP).

Communications in Theoretical PhysicsApr 1, 19920 citations

FINDING AND DISENTANGLING COMPLICATED UNITARY OPERATORS BY VIRTUE OF THE INTEGRATION OVER DIRAC'S KET–BRA OPERATORS

Hong-Yi Fan

Usually complicated unitary operators in exponential form are hard to handle and the transformation stated by them are not physically clear until these operators are disentangled. By virtue of the technique of integration within an ordered product (IWOP) of operators, we can disentangle some complicated unitary operators and then reveal their physical role. Many new unitary operators can be found after new quantum mechanical representations are constructed by virtue of the IWOP technique. The unitary operators for permutation, Hilbert transform, Householder transform, and Hardmad transform can also be introduced. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics and provides a new route connecting classical transformations to quantum mechanical unitary operators. In this way, the symbolic method exhibits further beauty and elegance and can be increasingly used for developing various fields of quantum physics.Usually complicated unitary operators in exponential form are hard to handle and the transformation stated by them are not physically clear until these operators are disentangled. By virtue of the technique of integration within an ordered product (IWOP) of operators, we can disentangle some complicated unitary operators and then reveal their physical role. Many new unitary operators can be found after new quantum mechanical representations are constructed by virtue of the IWOP technique. The unitary operators for permutation, Hilbert transform, Householder transform, and Hardmad transform can also be introduced. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics and provides a new route connecting classical transformations to quantum mechanical unitary operators. In this way, the symbolic method exhibits further beauty and elegance and can be increasingly used for developing various fields of quantum physics.

Modern Physics Letters BAug 20, 20084 citations

General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

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General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

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