NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

doi:10.1088/1009-1963/9/10/002

中国物理B ›› 2000, Vol. 9 ›› Issue (10): 726-730.doi: 10.1088/1009-1963/9/10/002

NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

梁先庭

Department of Physics and Institute of Mathematics, Huaihua Teachers College, Huaihua 418008, China

收稿日期:2000-02-15 修回日期:2000-06-08 出版日期:2000-12-25 发布日期:2005-06-10

NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

Liang Xian-ting (梁先庭)

Department of Physics and Institute of Mathematics, Huaihua Teachers College, Huaihua 418008, China

Received:2000-02-15 Revised:2000-06-08 Online:2000-12-25 Published:2005-06-10

摘要/Abstract

摘要： Based on the quantum mechanical representation |ξ〉=exp[\dfrac12|ξ|+ξ a⁺₁+ξ^* a⁺₂-a⁺₁a⁺₂]|00〉constructed by Fan Hong-yi and with the help of the technique of integration within an ordered product of operators, we derive the normally ordered expressions of the Shapiro-Wagner (SW) phase operators. They are in terms of the Bessel functions. As their application we discuss the minimal uncertain relation regarding the two-mode phase and number-difference operators.

Abstract: Based on the quantum mechanical representation $|\xi>$=exp$[-\frac12|\xi|$+$\xi a_1^+$ + $\xi^*a_2^+$ $-$ $a_1^+$ $a_2^+$] $|00>$ constructed by Fan Hong-yi and with the help of the technique of integration within an ordered product of operators, we derive the normally ordered expressions of the Shapiro-Wagner (SW) phase operators. They are in terms of the Bessel functions. As their application we discuss the minimal uncertain relation regarding the two-mode phase and number-difference operators.

Key words: SW phase operator, Bessel function, normally ordered product

中图分类号: (Linear algebra)

02.10.Ud

02.30.Cj (Measure and integration) 02.30.Gp (Special functions) 02.30.Tb (Operator theory) 03.65.Fd (Algebraic methods)

梁先庭. NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION[J]. 中国物理B, 2000, 9(10): 726-730.

Liang Xian-ting (梁先庭). NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION[J]. Chinese Physics, 2000, 9(10): 726-730.

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NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

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