Sökning: "Lieb-Thirring inequalities"
Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Lieb-Thirring inequalities.
1. Spectral Inequalities and Their Applications in Quantum Mechanics
Sammanfattning : The work presented in this thesis revolves around spectral inequalities and their applications in quantum mechanics.In Paper A, the ground state energy of an atom confined to two dimensions is analyzed in the limit when the charge of the nucleus Z becomes very large. LÄS MER
2. Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
Sammanfattning : This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators. In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator. LÄS MER
3. Spectral estimates for the magnetic Schrödinger operator and the Heisenberg Laplacian
Sammanfattning : I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. LÄS MER
4. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization
Sammanfattning : This thesis consists of eight papers primarily concerned with the quantitative study of the spectrum of certain differential operators. The majority of the results split into two categories. LÄS MER
5. Schrödinger Operators in Waveguides
Sammanfattning : In this thesis, which consists of four papers, we study the discrete spectrum of Schrödinger operators in waveguides. In these domains the quadratic form of the Dirichlet Laplacian operator does not satisfy any Hardy inequality. LÄS MER