Some Schrödinger operators with dense point spectrum
From MaRDI portal
Publication:5690934
DOI10.1090/S0002-9939-97-03559-4zbMath0888.34071OpenAlexW1750710615MaRDI QIDQ5690934
Publication date: 9 January 1997
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03559-4
Schrödinger operatorresonanceSturm-Liouville theoryhalf-bound statessubordinacygeneralized Prüfer transformationWigner-von Neumann eigenvalue theory
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)
Related Items
Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one, The spectral measure of a Jacobi matrix in terms of the Fourier transform of the perturbation, Schrödinger operators with \(n\) positive eigenvalues: an explicit construction involving complex-valued potentials, Zeroes of the spectral density of the periodic Schrödinger operator with Wigner–von Neumann potential, Twelve tales in mathematical physics: An expanded Heineman prize lecture, Topics on Fermi varieties of discrete periodic Schrödinger operators, Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials, Freezable bound states in the continuum for time-dependent quantum potentials, A new class of Schrödinger operators without positive eigenvalues, The absence of singular continuous spectrum for perturbed Jacobi operators, Dirac operators with operator data of Wigner-von Neumann type, On new relations between spectral properties of Jacobi matrices and their coefficients, Schrödinger operators with slowly decaying Wigner-von Neumann type potentials, On the existence of embedded eigenvalues, CORRUGATED SURFACES AND A.C. SPECTRUM, Absolutely continuous spectrum of Stark operators, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators, Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a. e. convergence of integral operators, Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian, On the absolutely continuous spectrum of Stark Hamiltonians, Schrödinger operators in the twentieth century, Tosio Kato's work on non-relativistic quantum mechanics. I, Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach, Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators, The equiconvergence problem for a one-dimensional Schrödinger operator with a uniformly locally integrable potential, Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials, Imbedded singular continuous spectrum for Schrödinger operators, Quantum quasiballistic dynamics and thick point spectrum, Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results, Tosio Kato’s work on non-relativistic quantum mechanics, Part 2, Classical and quantum integrability of hamiltonians without scattering states, Sharp bound for embedded eigenvalues of Dirac operators with decaying potentials, Schrödinger operators with decaying potentials: some counterexamples, Revisiting the Christ–Kiselev’s multi-linear operator technique and its applications to Schrödinger operators, Embedded singular continuous spectrum for one-dimensional Schrödinger operators, Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrödinger operators
Cites Work
- Unnamed Item
- Unnamed Item
- Asymptotic integration of adiabatic oscillators
- Product integrals II: Contour integrals
- Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
- The asymptotic solution of second-order differential equations
- Product integrals and the Schrödinger equation