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Phase space quantum mechanics - direct. (English) Zbl 1112.81069
Summary: Conventional approach to quantum mechanics in phase space, $\left(q,p\right)$, is to take the operator based quantum mechanics of Schrödinger, or an equivalent, and assign a $c$-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of $q$ and $p$ is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the $q$- or $p$-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.

##### MSC:
 81S30 Phase space methods in quantum mechanics