Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator with Singular Potentials

By Thomas Kappeler, C. Möhr. 2001

51 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91c1b93eeda710c61fdc925f834eee7915830edb

How researchers see this paper

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In Applied Mathematics

1. Y. Mykytyuk
2. Rostyslav Hryniv
3. Peter Perry
4. P. Topalov
5. Thomas Kappeler
6. S. Benenti

In Mathematical Physics

1. Y. Mykytyuk
2. Rostyslav Hryniv
3. P. Topalov
4. Thomas Kappeler

Citations in the corpus

• The Miura map on the line (2005, background): “See also [20], [21], [23], [29], [30], [37], [40], [41] as well as [41] for further references.”
• Transformation Operators for Sturm-Liouville Operators with Singular Potentials (2004, methodology): “For the Dirichlet eigenvalues, we generalise the related results of [18] in several ways: a wider class of potentials is treated (no periodicity is assumed and α = 0 is included), ε is removed in the relation (νn) ∈ l 2 for νn as in (1.”
• Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials (2006, background): “We observe that the considered class of singular potentials include Dirac δ-type and Coulomb 1/x-type interactions that are widely used in quantum mechanics and mathematical physics; see also [ 18 ] for other physical models leading to potentials from negative Sobolev spaces.”