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On spectral properties of the discrete Schrödinger operator with pure imaginary finite potential. (English. Russian original) Zbl 1177.35056
Math. Notes 85, No. 3, 437-440 (2009); translation from Mat. Zametki 85, No. 3, 451-455 (2009).
Summary: We consider the spectral properties of the discrete Schrödinger operator in the space of square integrable two-sided sequences with a pure imaginary potential of finite rank with zero mean value. We show that if such potentials are small, then the spectrum of the operator under study coincides with the spectrum of the unperturbed operator, and the operator itself is similar to a self-adjoint operator.
MSC:
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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