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arXiv:1209.1850 · Journal of Pseudo-Differential Operators and Applications

Quantum mechanics in phase space: the Schrödinger and the Moyal representations

Nuno Costa Dias, Maurice de Gosson, Franz Luef, João Nuno Prata

Published Sep 4, 2012• 12 citations
arXivHTMLPDF
DOI
10.1007/s11868-012-0054-9

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The phase space formulation of quantum mechanics is equivalent to standard quantum mechanics where averages are calculated by way of phase space integration as in the case of classical statistical mechanics. We derive the quantum hierarchy equations, often called the contracted Schrödinger equation, in the phase space representation of quantum mechanics which involves quasi-distributions of position and momentum. We use the Wigner distribution for the phase space function and the Moyal phase space eigenvalue formulation to derive the hierarchy. We show that the hierarchy equations in the position, momentum, and position-momentum representations are very similar in structure. © 2017 Wiley Periodicals, Inc.