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Communications in Theoretical Physics

Coordinate SchrSdinger Representation of Squeezing Operator for Scalar Field Gained via the IWOP Technique

Fan Hong‐Yi, Fan Yue

Published Sep 15, 2000• 1 citation
Publisher

Abstract

By deriving the Fock representation of Schr?dinger field operators' eigenvectors and using the technique of functional integration within an ordered product of operators we provide a direct route to obtaining normally ordered squeezing operator for scalar field, which is mathematically concise and physically appealing. The coordinate Schr?dinger representation of field squeezing operator is then obtained.

DOI
10.1088/0253-6102/34/2/373

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By deriving the Fock representation of Schr?dinger field operators' eigenvectors and using the technique of functional integration within an ordered product of operators we provide a direct route to obtaining normally ordered squeezing operator for scalar field, which is mathematically concise and physically appealing. The coordinate Schr?dinger representation of field squeezing operator is then obtained.
The state |x〉λ,v was derived by using the technique of integration within an ordered product of operators(IWOP)that was the eigenstate of two rotational quadrature components λQ^+vP of light field.The basic vector |x〉λ,v becomes a new quantum mechanics representation which is between coordinate representation and momentum representation.With the help of the new representation,we obtain the normal product of the operators exp[-f(λQ +vP )2] and(λQ+vP)n.Furthermore,we construct a new quantum unitary operator which is used on vacuum state can obtain a new quantum optics squeezing state.
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.