Finiteness of Eigenvalues for Operator Matrices Arising in Quantum Mechanics
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In this paper, an operator matrix of order three corresponding to a lattice system
with a non-conserved number of particles not exceeding three, arising in quantum mechanics is
considered as a linear, bounded, and self-adjoint operator acting in a Hilbert space. The essential
spectrum of the considered third-order operator matrix is investigated. The two-particle and three-
particle branches of the essential spectrum are identified. It is proved that, for an arbitrary value of
the spectral parameter, the discrete spectrum of the operator matrix is finite.
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