Self-similar solutions for nonlinear Schrödinger equations.
Semi-classical approximation and microcanonical ensemble
Semiclassical states for weakly coupled nonlinear Schrödinger systems
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Short waves through thin interfaces and 2-microlocal measures
Singular integrals of the time-harmonic relativistic Dirac equation on a piecewise Liapunov surface.
Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.
In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...
Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
Solitary waves for Maxwell-Schrödinger equations.
Solutions globales des systèmes de Dirac-Klein-Gordon
Solutions of the central Woods-Saxon potential in case using mathematical modification method.
Solutions of the Dirac-Fock equations without projector
In this paper we prove the existence of infinitely many solutions of the Dirac-Fock equations with electrons turning around a nucleus of atomic charge , satisfying and , where is the fundamental constant of the electromagnetic interaction (approximately 1/137). This work is an improvement of an article of Esteban-Séré, where the same result was proved under more restrictive assumptions on .
Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics.
Solvable two-body Dirac equation as a potential model of light mesons.
Sparse grids for the Schrödinger equation
We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...
Spectral analysis of relativistic atoms -- Dirac operators with singular potentials.
Spectral analysis of relativistic atoms -- interaction with the quantized radiation field.
Spectral Theory of the Dirac Operator.
Splitting of the Dirac operator in the nonrelativistic limit
Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field.
Stability of the Brown-Ravenhall operator.