Geodesic
Quadratic Integrals of Motion for Systems of Identical Particles: The Quantum Case
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 290-294

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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. 
@article{TMF_2005_144_2_a5,
     author = {Y. Brihaye and C. Gonera and P. Kosinski and P. Maslanka and S. Giller},
     title = {Quadratic {Integrals} of {Motion} for {Systems} of {Identical} {Particles:} {The} {Quantum} {Case}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a5/}
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Y. Brihaye; C. Gonera; P. Kosinski; P. Maslanka; S. Giller. Quadratic Integrals of Motion for Systems of Identical Particles: The Quantum Case. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 290-294. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a5/