The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The continuous Coupled Cluster formulation for the electronic Schrödinger equation
Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the stationary electronic Schrödinger equation. Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, i.e. within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis...
The Heun equation and the Calogero-Moser-Sutherland system. II: Perturbation and algebraic solution.
The initial value problem for the quadratic nonlinear Klein-Gordon equation.
The noncommutative Dirac equation for some wave functions.
The nonrelativistic limit of the nonlinear Dirac equation
The relation between Maxwell, Dirac, and the Seiberg-Witten equations.
The second-order Klein-Gordon field equation.
The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}
We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.
The symmetry algebra and conserved Currents for Klein-Gordon equation on quantum Minkowski space
The symmetry operators for Klein-Gordon equation on quantum Minkowski space are derived and their algebra is studied. The explicit form of the Leibniz rules for derivatives and variables for the case Z=0 is given. It is applied then with symmetry operators to the construction of the conservation law and the explicit form of conserved currents for Klein-Gordon equation.
The time-dependent Born-Oppenheimer approximation
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
The weak coupling limit without rotating wave approximation
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
There is no two dimensional analogue of Lamé's equation.
Time as a quantum observable, canonically conjugated to energy, and foundations of self-consistent time analysis of quantum processes.
Time decay of finite energy solutions of the non linear Klein-Gordon and Schrödinger equations
Transfer of conditions for singular boundary value problems
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...
Transient phenomena in quantum bound states subjected to a sudden perturbation.
Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1