Perturbation of the Spectrum of the one-Dimensional Self-Adjoint Schrödinger Operator with a Periodic Potential
It is well known that the spectrum of the one-dimensional Schrödinger operator with a periodic potential is purely continuous and consists of a countable sequence of segments of the real axis separated by lacunae and going out to + ∞. When this operator is perturbed by a real potential q(x) which vanishes at infinity, it is possible that eigenvalues will appear in the lacunae of the continuous spectrum and also to the left of the lower bound of the operator. The following facts are known.
KeywordsContinuous Spectrum Simple Root Piecewise Continuous Function Resolvent Kernel Schrodinger Operator
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