RUS  ENG
Полная версия
ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2008, том 13, выпуск 6, страницы 588–592 (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

Аннотация: 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.

Ключевые слова: Calogero–Moser systems, equilibrium points, Hill equation.

MSC: 33E05, 05E10, 37K60

Поступила в редакцию: 04.05.2008
Принята в печать: 15.06.2008

Язык публикации: английский

DOI: 10.1134/S1560354708060087



Реферативные базы данных:


© МИАН, 2024