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Contracted Schrödinger equation in quantum phase‐space
Author(s) -
Frishberg Carol,
Cohen Leon
Publication year - 2018
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.24883
Subject(s) - phase space , method of quantum characteristics , wigner distribution function , momentum (technical analysis) , position and momentum space , schrödinger equation , quantum mechanics , quantum statistical mechanics , position (finance) , physics , classical mechanics , eigenvalues and eigenvectors , mathematics , space (punctuation) , quantum dynamics , quantum , quantum process , linguistics , philosophy , finance , economics
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.