Improved sharp spectral inequalities for Schrödinger operators on the semi-axis. (English) Zbl 1529.34077
The author establishes a Lieb-Thirring inequality applicable to Schrödinger operators \(-\frac{d^2}{dx^2}+V\) represented on the semi-axis and subject to a Robin boundary condition at the origin. His findings present enhancements over the previously derived bounds outlined by P. Exner et al. [Commun. Math. Phys. 326, No. 2, 531–541 (2014; Zbl 1297.35155)], contingent upon an additional assumption \(V\in L^1 (R_+)\). His approach differs significantly by employing the double commutation method as opposed to the single commutation method utilized in prior studies. Additionally, he establishes an upgraded inequality specifically when dealing with a Dirichlet boundary condition.
Reviewer: Erdoğan Şen (Tekirdağ)
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 34B09 | Boundary eigenvalue problems for ordinary differential equations |
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
Keywords:
Robin boundary condition; Lieb-Thirring inequality; Schrödinger operator; commutation methodCitations:
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