Related papers: Born-Oppenheimer approximation for a harmonic mole…
We report on recent improvements to our non-perturbative calculation of the positronium spectrum. Our Hamiltonian is a two-body effective interaction which incorporates one-photon exchange terms, but neglects fermion self-energy effects.…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
We study magnetic traps with very high trap frequencies where the spin is coupled to the motion of the atom. This allows us to investigate how the Born-Oppenheimer approximation fails and how effective magnetic and electric fields appear as…
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the…
Thanks to an algebraic duality property of reduced states, the Schmidt best approximation theorems have important corollaries in the rigorous theory of two-electron moleculae. In turn, the "harmonium mode" or "Moshinsky atom" constitutes a…
We present a universal expression for the electronic friction as felt by a set of classical nuclear degrees of freedom (DoF's) coupled to a manifold of quantum electronic DoF's; no assumptions are made regarding the nature of the electronic…
Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pad\'e method (RPM). The convergence properties of the method are analyzed for different states. The…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
We discuss the usefulness of Born-Oppenheimer potential surfaces for nuclear dynamics for molecules strongly coupled to metal surfaces. A simple model demonstrating the construction of such surface for a molecular junction is discussed.
Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center of mass momentum $\bm{P}$ of the two particles and on the two relative momenta…
The use of plane wave approximation in molecular orbital tomography via high-order harmonic generation has been questioned since it was proposed, owing to the fact that it ignores the essential property of the continuum wave function. To…
We introduce a method to carry out zero-temperature calculations within density functional theory (DFT) but without relying on the Born-Oppenheimer (BO) approximation for the ionic motion. Our approach is based on the finite-temperature…
We define Sturmian basis functions for the harmonic oscillator and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many body problems such as coupling…
The calculations of the elementary atom (the Coulomb bound state of elementary particles) interaction with the atom of matter, which are performed in the Born approximation, are reviewed. We first discuss the nonrelativistic approach and…
This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear…
We are pursuing an experiment to measure the electric dipole moment of the electron using the molecule PbO. This measurement requires the ability to prepare quantum states with orientation of the molecular axis and, simultaneously,…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
The paper is a continuation of our previous work on the spatially homogeneous Boltzmann equation for Bose-Einstein particles with quantum collision kernel that includes the hard sphere model. Solutions $F_t$ under consideration that…
Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the…
We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic…