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.
Received: 15 February 2000
Revised: 08 June 2000
Accepted manuscript online:
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