Topics from spectral theory of differential operators
نویسندگان
چکیده
Introduction 2 1. Self-adjointness of Schrödinger operators 3 1.0. Solving the Schrödinger equation 3 1.1. Linear operators in Hilbert space 7 1.2. Criteria for (essential) self-adjointness 13 1.3. Application to Schrödinger operators 18 2. Hardy-Rellich inequalities 21 2.0. Relative boundedness 21 2.1. Weighted estimates 24 2.2. Explicit bounds 26 3. Spectral properties of radially periodic Schrödinger operators 28 3.0. Spectra of self-adjoint operators 29 3.1. Asymptotic behavior of eigensolutions and the spectrum 39 3.2. Spherical symmetry 40 3.2.1. Some basic examples 41 3.2.2. Embedded eigenvalues 43 3.3. Radial periodicity 44 3.3.1. Dense point spectrum 45 3.3.2. Welsh eigenvalues 46 3.4. Numerical analysis 47 References 49
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