Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field
arXiv:1102.0329 · doi:10.1007/s11005-011-0499-4
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.
12 pages