# Schrödinger operators with magnetic fields

@article{Avron1981SchrdingerOW, title={Schr{\"o}dinger operators with magnetic fields}, author={Joseph E. Avron and Ira W. Herbst and Barry Simon}, journal={Communications in Mathematical Physics}, year={1981}, volume={79}, pages={529-572} }

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 hasLz = 0 and of the monotonicity of the binding energy as a function ofB, (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…

## 445 Citations

### Atoms in Strong Magnetic Fields:¶The High Field Limit at Fixed Nuclear Charge

- Physics
- 1999

Abstract:Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as B→∞ with N and Z fixed…

### Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields II

- Mathematics, PhysicsNagoya Mathematical Journal
- 1997

This paper is continuation from [10], in which we studied the discrete spectrum of atomic Hamiltonians with non-constant magnetic fields and, more precisely, we showed that any atomic system has only…

### On the maximal ionization of atoms in strong magnetic fields

- Physics
- 2001

We give upper bounds for the number of spin-½ particles that can be bound to a nucleus of charge Z in the presence of a magnetic field B, including the spin-field coupling. We use Lieb's strategy,…

### Atoms in strong magnetic elds: The high eld limit at xed nuclear charge

- Physics
- 1999

Let E(B;Z;N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic eld B .W e study the asymptotics of E(B;Z;N )a sB!1with N and Z xed but…

### Simple diamagnetic monotonicities for Schrödinger operators with inhomogeneous magnetic fields of constant direction

- Physics
- 2002

Under certain simplifying conditions we detect monotonicity properties of the ground-state energy and the canonical-equilibrium density matrix of a spinless charged particle in the Euclidean plane…

### Lifshitz Tails in Constant Magnetic Fields

- Mathematics, Physics
- 2006

We consider the 2D Landau Hamiltonian H perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states…

### Exponential Localization of Hydrogen-like Atoms in Relativistic Quantum Electrodynamics

- Physics
- 2009

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second…

### Stability of Coulomb systems with magnetic fields

- Physics
- 1986

The analysis of the ground state energy of Coulomb systems interacting with magnetic fields, begun in Part I, is extended here to two cases. Case A: The many electron atom; Case B: One electron with…

### Scaling of the ground-state energy of relativistic ions in high locally bounded magnetic fields

- Physics
- 2010

We consider the pseudorelativistic Chandrasekhar/Herbst operator hH for the description of relativistic one-electron ions in a locally bounded magnetic field. We show that for Coulomb potentials of…

### Ground state solutions to Hartree–Fock equations with magnetic fields

- Physics
- 2018

ABSTRACT Within the Hartree–Fock theory of atoms and molecules, we prove existence of a ground state in the presence of an external magnetic field when: (1) the diamagnetic effect is taken into…

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