Journal of Computational Chemistry
Journal of Computational Chemistry
5 years ago

Contracted Schrödinger equation in quantum phase-space

Contracted Schrödinger equation in quantum phase-space
Leon Cohen, Carol Frishberg
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. The quantum hierarchy equations, often called the contracted Schrodinger equation, are standardly formulated in position space. We derive the hierarchy equations, in momentum space and also in quantum phase space where we use the Wigner distribution. We show that the hierarchy equations in the position, momentum, and position-momentum representations are very similar in structure.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/jcc.24883

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