Schrδdinger Operators With Magnetic Fields III. Atoms in Homogeneous Magnetic Field

We prove a large number of results about atoms in constant magnetic field including (i) Asymptotic formula for the ground state energy of Hydrogen in large field, (ii) Proof that the ground state of Hydrogen in an arbitrary constant field has Lz = 0 and of the monotonicity of the binding energy as a function of B, (iii) Borel summability of Zeeman series in arbitrary atoms, (iv) Dilation analyticity for arbitrary atoms with infinite nuclear mass, and (v) Proof that every once negatively charged ion has infinitely many bound states in non-zero magnetic field with estimates of the binding energy for small B and large Lz.