Geodesic
On the spectrum of the three-particle Hamiltonian on a~unidimensional lattice
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 3-22

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On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials. We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite. 
@article{MT_2014_17_2_a0,
     author = {N. M. Aliev and M. E. Muminov},
     title = {On the spectrum of the three-particle {Hamiltonian} on a~unidimensional lattice},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--22},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2014_17_2_a0/}
}
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N. M. Aliev; M. E. Muminov. On the spectrum of the three-particle Hamiltonian on a~unidimensional lattice. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 3-22. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a0/