On the solutions of multicomponent generalizations of the Lam{é} equation

Details On the solutions of multicomponent generalizations of the Lam{é} equation On the solutions of multicomponent generalizations of the Lam{é} equation

2008-04-21

arxiv.org/abs/0804.3090v1

Phys. Lett. A 372 (2008) 5951-5954

Physics

Mathematical Physics

8 pages, 1 table, no figures, revtex4

Scientific paper

10.1016/j.physleta.2008.07.067

We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling constant we propose the ansatz which allows one to get meromorphic solutions with two arbitrary parameters. They are quantized upon the requirement of the regularity of the wave function on the hyperplanes at which particles meet and imposing periodic boundary conditions. We find also the extra integrals of motion for three-particle systems which commute with the Hamiltonian for arbitrary values of the coupling constant.

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