Geodesic
On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schr\"odinger Operator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 56-60

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A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.
Keywords: Schrödinger equation, Faddeev integral equation.
Mots-clés : boson 
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     author = {S. A. Albeverio and S. N. Lakaev and Zh. I. Abdullaev},
     title = {On the {Finiteness} of the {Discrete} {Spectrum} of a {Four-Particle} {Lattice} {Schr\"odinger} {Operator}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     volume = {36},
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S. A. Albeverio; S. N. Lakaev; Zh. I. Abdullaev. On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schr\"odinger Operator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 56-60. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a5/