The 2D Schrödinger equation for a neutral pair in a constant magnetic field
The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms.
The difference equation related to the problem of the hydrogen atom in a strong magnetic field.
The essential spectrum of relativistic multi-particle operators
The essential spectrum of relativistic one-electron ions in the Jansen-Hess model.
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The ground state energy of relativistic one-electron atoms according to Jansen and Heß.
The Heun equation and the Calogero-Moser-Sutherland system. II: Perturbation and algebraic solution.
The level crossing problem in semi-classical analysis. II. The Hermitian case
This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.
The Mourre estimate for regular dispersive systems
The projected single-particle Dirac operator for Coulombic potentials.
The scattering problem for a noncommutative nonlinear Schrödinger equation.
The Schrödinger equation on non-stationary domains.
The spectral cutting problem
The spectral properties of the Schrödinger operator in nonseparable Hilbert spaces
The spectrum of Schrödinger operators with random magnetic fields
We shall consider the Schrödinger operators on with the magnetic field given by a nonnegative constant field plus random magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...
The Uncertainty Principle: A Mathematical Survey.
Three-Hilbert-space formulation of quantum mechanics.
Towards finite-gap integration of the Inozemtsev model.
Transfer matrices and transport for Schrödinger operators
We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....