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arXiv · 1208.2835

Canonical transformations in quantum mechanics

Maciej Blaszak·Ziemowit Domanski
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Abstract

This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when passing to a new coordinate system, observables and states transform as in classical mechanics, i.e., by composing them with a transformation of coordinates. Then the developed formalism of coordinate transformations is transferred to a standard formulation of quantum mechanics. In addition, the developed theory is illustrated on examples of particular classes of quantum canonical transformations.

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Maciej Blaszak, Ziemowit Domanski. 2012-08-14. Canonical transformations in quantum mechanics. https://doi.org/10.1016/j.aop.2012.12.006

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