Y. Brihaye, C. Gonera, P. Kosinski, P. Maslanka, S. Giller, “Quadratic Integrals of Motion for Systems of Identical Particles: The Quantum Case”, TMF, 2005, Volume 144, Number 2,Pages <nobr>290

Quadratic Integrals of Motion for Systems of Identical Particles: The Quantum Case

Y. Brihaye^a, C. Gonera^b, P. Kosinski^b, P. Maslanka^b, S. Giller^c

^a Université de Mons–Hainaut
^b University of Łódź
^c Pedagogical University of Częstochowa

Abstract: We consider the quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta and find that an appropriate ordering procedure exists that allows converting the classical integrals into their quantum counterparts. We discuss the relation to the separation of variables in the Schrodinger equation.

Keywords: quantum integrals of motion, Calogero–Sutherland–Moser models, separation of variables, $sl(2,\mathbb{R})$ symmetry.

DOI: 10.4213/tmf1853