On eigenvalues of the discrete Schrödinger operator on a ladder of a d-dimensional square lattice

We consider a discrete Schrödinger operator H on a ladder of d-dimensional square lattices with a self-adjoint matrix-valued potential whose entries are the scalars λ and µ. We investigate conditions for the existence of eigenvalues and describe their exact locations in terms of the parameters λ and µ for the cases d = 1 and d = 2.

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