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Quantum theory --- Schrödinger operator --- Spectral theory (Mathematics) --- Partial differential operators --- Théorie quantique. --- Schrödinger, Opérateur de. --- Théorie spectrale (mathématiques) --- Opérateurs différentiels partiels.

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The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.

Operator theory --- Mathematical physics. --- Perturbation (Mathematics). --- Perturbation (Quantum dynamics). --- Schrödinger operator. --- Schrodinger operator. --- Perturbation (Quantum dynamics) --- Perturbation (Mathematics) --- Mathematical physics --- Schrèodinger operator --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Mathematische fysica --- Perturbatie (Wiskunde) --- Perturbation (Dynamique quantique) --- Perturbation (Mathématiques) --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Schrödinger [Operateur de ] --- Schrödinger operator --- Schrödingeroperator --- Storing (Quantumdynamica) --- Wiskundige fysica --- Partial differential equations. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Physics --- Partial differential equations