The Ehrenfest system and the rest point spectrum for a Hartree-type Equation

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dc.creatorBelov, V. V.
dc.creatorKondratieva, M. F.
dc.creatorTrifonov, A. Yu.
dc.date2005-10-31
dc.date2005-12-31
dc.date.accessioned2026-07-07T06:47:06Z
dc.date.available2026-07-07T06:47:06Z
dc.descriptionFollowing Ehrenfest's approach, the problem of quantum-classical correspondence can be treated in the class of trajectory-coherent functions that approximate as $\h\to 0$ a quantum-mechanical state. This idea leads to a family of systems of ordinary differential equations, called Ehrenfest M-systems (M=0,1,2,...), formally equivalent to the semiclassical approximation for the linear Schroedinger equation. In this paper a similar approach is undertaken for a nonlinear Hartree-type equation with a smooth integral kernel. It is demonstrated how quantum characteristics can be retrieved directly from the corresponding Ehrenfest systems, without solving the quantum equation: the semiclassical asymptotics for the spectrum are obtained from the rest point solution. One of the key steps is derivation of a modified nonlinear superposition principle valid in the class of trajectory-coherent quantum states.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0510096
dc.identifierhttp://arxiv.org/abs/math-ph/0510096
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103548
dc.subjectMathematical Physics
dc.titleThe Ehrenfest system and the rest point spectrum for a Hartree-type Equation
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