Related papers: Born-Oppenheimer approximation for a harmonic mole…
Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here,…
Extended Lagrangian Born-Oppenheimer molecular dynamics [{\em Phys.\ Rev.\ Lett.\ } {\bf 2008}, {\em 100}, 123004] is presented for Hartree-Fock theory, where the extended electronic degrees of freedom are represented by a density matrix,…
We study nonlinear n-term approximation of harmonic functions on the unit ball in $R^d$ from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Laplace equation) in BMO. A sharp Jackson estimate is…
We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation,…
While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of…
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the…
We establish a correspondence between the electric dipole matrix elements of a polyatomic symmetric top molecule in a state with nonzero projection of the total angular momentum on the symmetry axis of the molecule and the magnetic dipole…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present…
High-precision measurements of violations of fundamental symmetries in atoms are a very effective means of testing the standard model of elementary particles and searching for new physics beyond it. Such studies complement measurements at…
The Born approximation of a potential in the context of the Calder\'on inverse problem is an object that can be formally defined in terms of spectral data of the Dirichlet-to-Neumann map of the corresponding Schr\"odinger operator. In this…
In this work, we refine the Bohr model of the hydrogen atom by describing the motion of the electron through a single real-valued stochastic process, effectively realizing Brownian motion under the Born rule. Our approach derives the…
A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an…
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of the relativistic quantum mechanics, the…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous…
We solve a general equation describing the lowest order corrections arising from quantum gravitational effects to the spectrum of cosmological fluctuations. The spectra of scalar and tensor perturbations are calculated to first order in the…