Construction of the phase operator using logarithm of the annihilation operator

Details Construction of the phase operator using logarithm of the annihilation operator Construction of the phase operator using logarithm of the annihilation operator

2010-06-27

arxiv.org/abs/1006.5211v3

Physics

Mathematical Physics

7 pages

Scientific paper

We investigate a lema that excludes existence of the phase operator and present a condition to avoid the lema. A method for construction of an analytic function 'f' of the annihilation operator 'a' is given. f(z) is analytic on some compact domain that does not separate the complex plane. Using these results we obtain ln a. Since [N ,-i ln a]=i, we can use ln a to construct an operator $\Phi$, which satisfies the definition of the phase operator.

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