Asymptotics of Eigenvalues of the Two-particle Schrödinger operators on lattices

Details Asymptotics of Eigenvalues of the Two-particle Schrödinger operators on lattices Asymptotics of Eigenvalues of the Two-particle Schrödinger operators on lattices

2010-10-12

arxiv.org/abs/1010.2348v1

J.Phys.A44:135304,2011

Physics

Mathematical Physics

Scientific paper

10.1088/1751-8113/44/13/135304

The Hamiltonian of a system of two quantum mechanical particles moving on the $d$-dimensional lattice $\Z^d$ and interacting via zero-range attractive pair potentials is considered. For the two-particle energy operator $H_{\mu}(K),$ $K\in \T^d=(-\pi,\pi]^d$ -- the two-particle quasi-momentum, the existence of a unique positive eigenvalue $z(\mu, K)$ above the upper edge of the essential spectrum of $H_{\mu}(K)$ is proven and asymptotics for $z(\mu, K)$ are found when $\mu$ approaches to some $\mu_0(K)$ and $K\to 0.$

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