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arXiv · 1103.3132

On the discrete spectrum of two-particle discrete Schrödinger operators

Z. I. Muminov
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Abstract

In the present paper our aim is to explore some spectral properties of the family two-particle discrete Schrödinger operators $h^{\mathrm{d}}(k)=h^{\mathrm{d}}_0(k)+ \mathbf{v},$ $k\in \T^\mathrm{d},$ on the $\mathrm{d}$ dimensional lattice $\Z^{\mathrm{d}},$ $\mathrm{d}\geq 1,$ $k$ being the two-particle quasi-momentum. Under some condition in the case $k\in \T^{\mathrm{d}}\setminus (-π,π)^{\mathrm{d}},$ we establish necessary and sufficient conditions for existence of infinite discrete spectrum of the operator $h^{\mathrm{d}}(k)$.

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Z. I. Muminov. 2011-03-16. On the discrete spectrum of two-particle discrete Schrödinger operators. https://arxiv.org/abs/1103.3132

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