Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials
Copyright policy )Spectral Asymptotics for the Schrödinger Operator on the Line with Spreading and Oscillating Potentials
This study is devoted to the asymptotic spectral analysis of multiscale Schrödinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal form filtrating most of the oscillations, a reduction to a non-oscillating effective Hamiltonian is performed.
Schrödinger operator, rapid oscillations, WKB expansion, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, [MATH] Mathematics [math], 34L40, 34E10, 510, Mathematics - Spectral Theory, Perturbations, asymptotics of solutions to ordinary differential equations, 34L15, normal form, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Spectral Theory (math.SP), spectral asymptotics
Schrödinger operator, rapid oscillations, WKB expansion, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, [MATH] Mathematics [math], 34L40, 34E10, 510, Mathematics - Spectral Theory, Perturbations, asymptotics of solutions to ordinary differential equations, 34L15, normal form, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Spectral Theory (math.SP), spectral asymptotics
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