带干扰项的全概率公式及上下文Kolmogorovian模型的希尔伯特空间表示
A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorovian model
摘要：
我们比较了经典Kolmogorov模型和量子概率模型。我们发现，这些模型之间的差距并不像人们普遍认为的那样巨大。量子理论的主要结构（概率干涉、玻恩规则、复概率振幅、希尔伯特状态空间、用算子表示观测量）都以潜在形式存在于柯尔莫哥洛夫模型中。特别是，我们得到“干扰的概率”，而不诉诸希尔伯特空间形式主义。我们将“概率干扰”解释为对总概率常规公式的扰动（通过$\cos$项）。量子概率形式主义的经典推导可以促进量子方法在微观世界之外的应用：在心理学，生物学，经济学等领域。
英文摘要：
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the Kolmogorov model. In particular, we obtain ``interference of probabilities'' without to appeal to the Hilbert space formalism. We interpret ``interference of probabilities'' as a perturbation (by a $\cos$-term) of the conventional formula of total probability. Our classical derivation of quantum probabilistic formalism can stimulate applications of quantum methods outside of microworld : in psychology, biology, economy,...
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