Abstract
We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice \(\mathbb{Z}^{3}\) with a finite spherically symmetric potential. It is proven that the corresponding Shrödinger operator \(H(\mathbf{k}),\) where \(\mathbf{k}\in(-\pi,\pi]^{3}\) is the total quasimomentum of the system, has four invariant subspaces \(L_{123}^{-},\,\,L_{1}^{-},\,\,L_{2}^{-},\,\,L_{3}^{-}\) and it has no eigenfunctions in \(L_{123}^{-}\). We also show that the operator \(H(\mathbf{\Lambda}),\,\,\mathbf{\Lambda}=(\pi-2\lambda,\pi-2\lambda,\pi-2\lambda)\) has four different threefold eigenvalues for small \(\lambda\).
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Abdullaev, J.I., Toshturdiev, A.M. Invariant Subspaces of the Shrödinger Operator with a Finite Support Potential. Lobachevskii J Math 43, 728–737 (2022). https://doi.org/10.1134/S1995080222060026
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DOI: https://doi.org/10.1134/S1995080222060026