Geodesic
A Generalized Coordinate-Momentum Representation in Quantum Mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 401-416

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We obtain a one-parameter family of $(q,p)$-representations of quantum mechanics; the Wigner distribution function and the distribution function we previously derived are particular cases in this family. We find the solutions o the evolution equations or the microscopic classical and quantum distribution functions in the form of integrals over paths in a phase space. We show that when varying canonical variables in the Green's function of the quantum Liouville equation, we must use the total increment o the action functional in its path-integral representation, whereas in the Green's function of the classical Liouville equation, the linear part o the increment is sufficient. A correspondence between the classical and quantum schemes holds only under a certain choice of the value of the distribution family parameter. This value corresponds to the distribution unction previously found.
Keywords: $(q,p)$-representation, path integral.
Mots-clés : Liouville equation 
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     author = {L. S. Kuz'menkov and S. G. Maksimov},
     title = {A {Generalized} {Coordinate-Momentum} {Representation} in {Quantum} {Mechanics}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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L. S. Kuz'menkov; S. G. Maksimov. A Generalized Coordinate-Momentum Representation in Quantum Mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 401-416. http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a5/