A Generalized Coordinate-Momentum Representation in Quantum Mechanics

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 of the evolution equations for 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 of the action functional in its path-integral representation, whereas in the Green's function of the classical Liouville equation, the linear part of 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 function previously found.

Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. I. Dielectric permeability tensor for magnetized plasmas

“…Some of them do not include the spin evolution [38,39,[41][42][43][44], but consider the exchange part of the Coulomb interaction [39], [44], or consider non-ideal plasmas with strong interaction [40], [41].…”

“…For further analysis it is useful to distinguish a part of conductivity tensor caused by the current σ αβ 1 (ω)δE β = q e m p α δf dp (42) and another part caused by the curl of magnetization σ αβ 2 (ω)δE β = ıµ e c ε αβγ k β δS γ dp.…”

Local equilibrium approach for fermi systems and quantum hydrodynamics

“…In previous work [4,8], we demonstrated that the problem of obtaining such an operator function has a unique solution, and the quantum analogue of function (1) corresponds to function (4) with the coefficients ϭ 1 and ϭ 0. This operator function has the form…”

“…[4,8]). Moreover, the following relations between the function F q and the hydrodynamic moments ⌸ ␣ 1 .…”

On kinetic description of electromagnetic processes in a quantum plasma

“…The interest in quantum plasmas -plasmas with quantum effects playing a significant role in their collective behavior -has considerably increased in the recent decade, during which a significant number of publications appeared on this subject (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12] and references therein). This surge of interest can primarily be associated with the recent progress in manufacturing and manipulation of metallic and semiconductor nanostructures, whose properties are to a large extent governed by collective (plasma) effects of their electron (and hole) population.…”