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This article is cited in 8 scientific papers (total in 9 papers)
Quasi-classical asymptotics of quasi-particles
V. P. Maslov, A. S. Mishchenko M. V. Lomonosov Moscow State University
Abstract:
The $n$-particle problem of the Schrodinger–Laplace–Beltrami equation on a manifold with an arbitrary interaction potential between particles is studied. A pseudodifferential operator $(\operatorname {mod}h^\infty )$ on the manifold is obtained that describes the energy level of the Hamiltonian for a self-consistent field. The equations for a quasi-particle are the variational equations for the non-linear Wigner equation corresponding to the Hartree equation. Expressions are obtained for both the asymptotics of the steady-state Wigner–Hartree equation corresponding to an energy level in the ergodic situation, and the asymptotics of a generalized eigenfunction of the variational equation corresponding to the same energy level manifold. The asymptotic recursion relations for the indicated problem in the case studied by Bogolyubov reduce to his results.
Received: 18.04.1997
Citation:
V. P. Maslov, A. S. Mishchenko, “Quasi-classical asymptotics of quasi-particles”, Sb. Math., 189:6 (1998), 901–930
Linking options:
https://www.mathnet.ru/eng/sm325https://doi.org/10.1070/sm1998v189n06ABEH000325 https://www.mathnet.ru/eng/sm/v189/i6/p85
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