Moyal bracket

Quantum mechanics
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$i\hbar {\frac {d}{dt}}\|\Psi \rangle ={\hat {H}}\|\Psi \rangle$ Schrödinger equation
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In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product.

The Moyal bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a lengthy dispute with Paul Dirac.^[1]^[2] In the meantime this idea was independently introduced in 1946 by Hip Groenewold.^[3]

^ Moyal, J. E.; Bartlett, M. S. (1949). "Quantum mechanics as a statistical theory". Mathematical Proceedings of the Cambridge Philosophical Society. 45 (1): 99–124. Bibcode:1949PCPS...45...99M. doi:10.1017/S0305004100000487. S2CID 124183640.
^ Moyal, Ann (2006). Maverick Mathematician: The Life and Science of J.E. Moyal (Chap. 3: Battle With A Legend). doi:10.22459/MM.08.2006. ISBN 9781920942595. Retrieved 2010-05-02.
^ Groenewold, H. J. (1946). "On the principles of elementary quantum mechanics". Physica. 12 (7): 405–460. Bibcode:1946Phy....12..405G. doi:10.1016/S0031-8914(46)80059-4.

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Moyal bracket

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