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- Phase_space_formulation abstract "The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space. In contrast, the Schrödinger picture uses the position or momentum representations (see also position and momentum space). The two key features of the phase space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product. The theory was fully detailed by Hip Groenewold in 1946 in his PhD thesis, with significant parallel contributions by Joe Moyal, each building off earlier ideas by Hermann Weyl and Eugene Wigner.The chief advantage of the phase space formulation is that it makes quantum mechanics appear as similar to Hamiltonian mechanics as possible by avoiding the operator formalism, thereby "'freeing' the quantization of the 'burden' of the Hilbert space." This formulation is statistical in nature and offers logical connections between quantum mechanics and classical statistical mechanics, enabling a natural comparison between the two (cf. classical limit). Quantum mechanics in phase space is often favored in certain quantum optics applications (see optical phase space), or in the study of decoherence and a range of specialized technical problems, though otherwise the formalism is less commonly employed in practical situations.The conceptual ideas underlying the development of quantum mechanics in phase space have branched into mathematical offshoots such as deformation theory (cf. Kontsevich quantization formula) and noncommutative geometry.".
- Phase_space_formulation wikiPageID "36053570".
- Phase_space_formulation wikiPageRevisionID "606522476".
- Phase_space_formulation caption "Time evolution of combined ground and 1st excited state Wigner function for the simple harmonic oscillator. Note the rigid motion in phase space corresponding to the conventional oscillations in coordinate space.".
- Phase_space_formulation caption "Wigner function for the harmonic oscillator ground state, displaced from the origin of phase space, i.e., a coherent state. Note the rigid rotation, identical to classical motion: this is a special feature of the SHO, illustrating the correspondence principle. From the general pedagogy web-site.".
- Phase_space_formulation hasPhotoCollection Phase_space_formulation.
- Phase_space_formulation image "DisplacedGaussianWF.gif".
- Phase_space_formulation image "TwoStateWF.gif".
- Phase_space_formulation position "center".
- Phase_space_formulation width "125".
- Phase_space_formulation width "230".
- Phase_space_formulation subject Category:Foundational_quantum_physics.
- Phase_space_formulation subject Category:Hamiltonian_mechanics.
- Phase_space_formulation subject Category:Mathematical_quantization.
- Phase_space_formulation subject Category:Quantum_mechanics.
- Phase_space_formulation subject Category:Symplectic_geometry.
- Phase_space_formulation comment "The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space. In contrast, the Schrödinger picture uses the position or momentum representations (see also position and momentum space). The two key features of the phase space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.".
- Phase_space_formulation label "Phase space formulation".
- Phase_space_formulation sameAs m.0j_3qfz.
- Phase_space_formulation sameAs Q7180966.
- Phase_space_formulation sameAs Q7180966.
- Phase_space_formulation wasDerivedFrom Phase_space_formulation?oldid=606522476.
- Phase_space_formulation isPrimaryTopicOf Phase_space_formulation.
