Canonical transformations in quantum mechanics
arXiv:1208.2835 · doi:10.1016/j.aop.2012.12.006
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.
26 pages
References in corpus (7)
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Cited by in corpus (6)
- Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
- Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure
- Deformation quantization of the Pais-Uhlenbeck fourth order oscillator
- Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator
- Natural star-products on symplectic manifolds and related quantum mechanical operators
- Poisson bracket operator