Counting eigenvalues of Schrödinger operators using the landscape function
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Publication:6203845
DOI10.4171/jst/488arXiv2306.03936OpenAlexW4392058001MaRDI QIDQ6203845
Richard Froese, Severin Schraven, Sven Bachmann
Publication date: 8 April 2024
Published in: Journal of Spectral Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2306.03936
Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Operators arising in mathematical physics (47B93)
Cites Work
- 100 years of Weyl's law
- An optimal Poincaré inequality for convex domains
- Nonclassical eigenvalue asymptotics
- Some quantum operators with discrete spectrum but classically continuous spectrum
- The landscape law for the integrated density of states
- Harnack inequality and continuity of solutions to elliptic equations with nonstandard growth conditions and lower order terms
- Estimates of the spectrum of the Schrödinger operator
- On the \(\bar {\partial{}}\) equation in weighted \(L^ 2\) norms in \(\mathbb{C} ^ 1\)
- Parametrix construction for a class of subelliptic differential operators
- Weak type estimates for singular values and the number of bound states of Schrödinger operators
- Fundamental matrices and Green matrices for non-homogeneous elliptic systems
- On fundamental solutions of generalized Schrödinger operators
- Comportement asymptotique des valeurs propres d'opérateurs du type Schrödinger à potentiel dégénérée
- \(L^ p\) estimates for Schrödinger operators with certain potentials
- On bounds of \(N(\lambda)\) for a magnetic Schrödinger operator
- The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions
- Łojasiewicz gradient inequalities for polynomial functions and some applications
- The landscape law for tight binding Hamiltonians
- Calogero type bounds in two dimensions
- Negative eigenvalues of two-dimensional Schrödinger operators
- Spectral theory of operators related to representations of nilpotent groups
- Upper and lower limits for the number of bound states in a given central potential
- Cwikel's theorem and the CLR inequality
- Cwikel's bound reloaded
- Quantitative bounds versus existence of weakly coupled bound states for Schrödinger type operators
- Localization of quantum states and landscape functions
- The uncertainty principle
- Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
- Bounds on the eigenvalues of the Laplace and Schroedinger operators
- The effective potential of an M-matrix
- Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities
- Regularized potentials of Schrödinger operators and a local landscape function
- Exponential decay estimates for fundamental solutions of Schrödinger-type operators
- Localization of eigenfunctions via an effective potential
- On negative eigenvalues of two‐dimensional Schrödinger operators
- Approximating the ground state eigenvalue via the effective potential
- The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius
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