Geodesic
Bound states of a system of two fermions on a one-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 47-57
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We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of bound states $N(k)$ is a nondecreasing function of the total quasimomentum of the system $k\in[0,\pi]$. We describe the set of discontinuity points of $N(k)$ and evaluate the jump $N(k+0)-N(k)$ at the discontinuity points. We establish that the bound-state energy $z_n(k)$ increases as the total quasimomentum $k\in[0,\pi]$ increases.
Keywords: Hamiltonian, bound state, total quasimomentum, Schrödinger operator, eigenvalue, resonance, Birman–Schwinger principle. 
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Zh. I. Abdullaev. Bound states of a system of two fermions on a one-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 47-57. http://geodesic.mathdoc.fr/item/TMF_2006_147_1_a2/

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