Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field

Details Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field

2011-02-02

arxiv.org/abs/1102.0329v1

Lett. Math. Phys. 97 (2011), no. 3, 227 - 241

Mathematics

Spectral Theory

12 pages

Scientific paper

We prove Lieb-Thirring inequalities for Schr\"odinger 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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