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This article is cited in 1 scientific paper (total in 1 paper)
A Generalized Coordinate-Momentum Representation in Quantum Mechanics
L. S. Kuz'menkova, S. G. Maksimovb a M. V. Lomonosov Moscow State University, Faculty of Physics
b Instituto Tecnologico de Morelia
Abstract:
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, Liouville equation, path integral.
Received: 22.11.2004 Revised: 20.01.2005
Citation:
L. S. Kuz'menkov, S. G. Maksimov, “A Generalized Coordinate-Momentum Representation in Quantum Mechanics”, TMF, 143:3 (2005), 401–416; Theoret. and Math. Phys., 143:3 (2005), 821–835
Linking options:
https://www.mathnet.ru/eng/tmf1821https://doi.org/10.4213/tmf1821 https://www.mathnet.ru/eng/tmf/v143/i3/p401
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