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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 6, Pages 588–592
DOI: https://doi.org/10.1134/S1560354708060087
(Mi rcd603)
 

JÜRGEN MOSER – 80

Equilibrium points of classical integrable particle systems, factorization of wave functions of their quantum analogs and polynomial solutions of the Hill equation

V.I. Inozemtsev

Joint Institute for Nuclear Research, Dubna, 141980, Moscow Region, Russia
Abstract: The relation between the characteristics of the equilibrium configurations of the classical Calogero–Moser integrable systems and properties of the ground state of their quantum analogs is found. It is shown that under the condition of factorization of the wave function of these systems the coordinates of classical particles at equilibrium are zeroes of the polynomial solutions of the second-order linear differential equation. It turns out that, under these conditions, the dependence of classical and quantum minimal energies on the parameters of the interaction potential is the same.
Keywords: Calogero–Moser systems, equilibrium points, Hill equation.
Received: 04.05.2008
Accepted: 15.06.2008
Bibliographic databases:
Document Type: Personalia
MSC: 33E05, 05E10, 37K60
Language: English
Citation: V.I. Inozemtsev, “Equilibrium points of classical integrable particle systems, factorization of wave functions of their quantum analogs and polynomial solutions of the Hill equation”, Regul. Chaotic Dyn., 13:6 (2008), 588–592
Citation in format AMSBIB
\Bibitem{Ino08}
\by V.I. Inozemtsev
\paper Equilibrium points of classical integrable particle systems, factorization of wave functions of their quantum analogs and polynomial solutions of the Hill equation
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 6
\pages 588--592
\mathnet{http://mi.mathnet.ru/rcd603}
\crossref{https://doi.org/10.1134/S1560354708060087}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2465726}
\zmath{https://zbmath.org/?q=an:1229.37123}
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