Related papers: The Born Oppenheimer wave function near level cros…
Bloch equations give a quantum description of the coupling between an atom and a driving electric force. In this article, we address the asymptotics of these equations for high frequency electric fields, in a weakly coupled regime. We prove…
The Glauber method is extensively used to describe the motion of a hadronic projectile in interaction with the surrounding nuclear medium. One of the main approximations consists in the linearization of the wave equation for the interacting…
In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role. We…
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…
Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasi-energies is obtained, which shows…
Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schr\"odinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without…
The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small…
The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars.…
The Rosenfeld functional provides excellent results for the prediction of the fluid phase of hard convex particle systems but fails beyond the freezing point. The reason for this limitation is the neglect of orientational and distance…
We analyze the entanglement between electronic and nuclear motions in molecular wave functions, by using different widely used ansatzes in molecular Hamiltonian models (H$^+_2$ in 1D and the Shin-Metiu model); namely, i) Born-Oppenheimer…
The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the…
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenheimer molecular dynamics, of the ground state, depends on the…
The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, $k_BT/e = 25$ mV. In nonlinear…
We report an infinite number of orthonormal wave functions bases for the quantum problem of a free particle in presence of an applied external magnetic field. Each set of orthonormal wave functions (basis) is labeled by an integer $p$,…
In order to include a correction by the Coulomb interaction in Bose-Einstein correlations (BEC), the wave function for the Coulomb scattering were introduced in the quantum optical approach to BEC in the previous work. If we formulate the…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
High magnetic fields in neutron stars, B ~ 10^{11} - 10^{13} G, substantially modify the properties of atoms and their interaction with radiation. In particular, the photoionization cross section becomes anisotropic and strongly…
The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and…