The representation of the power number operator aN was proposed,where a is a non-negative real number,aN is densely defined in L2(M),which the space of the square-integrable Bernoulli functional noise.The following conclusions are obtained:the first one was the spectral representation,where {an;n≥0} is the spectrum of aN,and the eigenvectors of aN constituted a standard orthogonal basis of L2(M);aN could be represented by the QNBs of L2(M);the vacuum state representation of aN was given using the vacuum state Zφas well as(Γ)-QNBs;obtained with the help of the(Γ)-QNBs{∂σn;n≥0}.The constructure of the composition of aN and {∂σ,∂*σ;σ∈(Γ)} was considered.
关键词
a级幂计数算子/算子表示/(Γ)量子Bernoulli噪声
Key words
a power number operator/operator representation/(Γ)quantum Bernoulli noise
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