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Schrödinger operator. --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation

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This invaluable book presents reviews of some recent topics in the theory of Schrödinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrödinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion)with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of thefunctional integral. The material is accessible to graduate studen

Schrödinger operator. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation --- Schrodinger operator.

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Operator theory --- Schrödinger operator --- Spectral theory (Mathematics) --- Schrodinger operator --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation --- Schrödinger operator --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics)

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Operator theory --- Random operators. --- Schrodinger operator. --- Spectral theory (Mathematics) --- 51 --- Random operators --- Schrodinger operator --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Operator, Schrödinger --- Differential operators --- Quantum theory --- Schrödinger equation --- Operators, Random --- Stochastic analysis --- Mathematics --- 51 Mathematics --- Schrödinger operator

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Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all – provided one is familiar with the theory of self-adjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum.

Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Schrödinger operator. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Operator, Schrödinger --- Mathematics. --- Operator theory. --- Operator Theory. --- Mathematics, general. --- Physics --- Mechanics --- Thermodynamics --- Differential operators --- Quantum theory --- Schrödinger equation --- Math --- Science --- Functional analysis --- Schrodinger operator.