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arXiv · 1102.0329

Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field

Rupert L. Frank·Rikard Olofsson
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Abstract

We prove Lieb-Thirring inequalities for Schrödinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.

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Rupert L. Frank, Rikard Olofsson. 2011-02-02. Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. https://doi.org/10.1007/s11005-011-0499-4

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