Geodesic
Spectrum of the~three-particle Schr\"odinger operator on a~one-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 387-403

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We consider a system of three arbitrary quantum particles on a one-dimensional lattice interacting pairwise via attractive contact potentials. We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum in the case where the masses of two particles are finite. We show that the discrete spectrum of the Schrödinger operator is infinite in the case where the masses of two particles in a three-particle system are infinite.
Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator. 
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     author = {M. \'E. Muminov and N. M. Aliev},
     title = {Spectrum of the~three-particle {Schr\"odinger} operator on a~one-dimensional lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--403},
     publisher = {mathdoc},
     volume = {171},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a2/}
}
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M. É. Muminov; N. M. Aliev. Spectrum of the~three-particle Schr\"odinger operator on a~one-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 387-403. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a2/