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Discrete Spectrum for a Periodic Schroedinger Operator Perturbed by a Decreasing Potential

S. V. Khryashchev

Abstract

One studies a periodic Schroedinger operator in L 2 (ℝ) perturbed by a potential decreasing at infinity in the mean.Criteria of infinitude and finiteness of the discrete spectrum in gaps are given. Similar results for a semiinfinite gap of the perturbed periodic Schroedinger operator in L 2 (ℝ n ),n≥3, are obtained.

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Available abstract

Key concepts: Schrödinger's cat, Operator (biology), Discrete spectrum, Spectrum (functional analysis), Periodic potential, Infinity, Mathematics, Mathematical analysis