Related papers: Born-Oppenheimer potential for H$_2$
We investigate the structure of a prototypical two-state conical intersection (BeH$_2$) using a phase space electronic Hamiltonian $\hat{H}_{PS}(\bR,\bP)$ that goes beyond the Born-Oppenheimer framework. By parameterizing the electronic…
We investigate the cosmological inflation for the Einstein-Hilbert action plus the Higgs potential function and the Gauss-Bonnet term coupled with the Higgs scalar field through a dilaton-like coupling. Then, using the…
Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the…
We calculate the lowest-order corrections to the static potential for both the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-like model, in the presence of a constant external magnetic field. Our analysis is carried out…
We use the two-electron wavefunctions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function for a uniform electron gas. We find excellent…
A sixth-order quadrupole boson Hamiltonian is used to describe the states $0^+$ and $2^+$ identified in several nuclei by various types of experiments. Two alternative descriptions of energy levels are proposed. One corresponds to a…
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…
We employ one-loop scattering amplitudes in Einstein-Maxwell theory to compute the classical Hamiltonian of a binary system of two charged, non-spinning compact objects. The Hamiltonian is valid to all orders in velocity and up to second…
The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the…
Accurate absolute level energies of the $B\,^1\Sigma^{+}_{u}$, $v=0-8, N$ and $EF\,^{1}\Sigma^{+}_{g}$, $v=0-21, N$ rovibrational quantum states of molecular deuterium are derived by combining results from a Doppler-free two-photon laser…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
For the general two-Higgs doublet model with Yukawa sector of type II (type II 2HDM), the Higgs alignment limit conditions are obtained for the neutral Higgs bosons with indefinite CP-parity $h_1, h_2$ or $h_3$, based on the symbolic…
Existence of a spectral singularity (SS) in the spectrum of {a Schr\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential…
We demonstrate the ability to extract a spin-entangled state of two neutral atoms via postselection based on a measurement of their spatial configuration. Typically, entangled states of neutral atoms are engineered via atom-atom…
The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us…
The loop induced coupling of an intermediate mass Higgs boson to two photons is a sensitive and unique measure for precision tests of physics beyond the Standard Model. In this work we summarize recent results on the expected precision of…
The inverse power potential $U(r)=r^{-1/s}, 0<s<1$, generates the Boltzmann kernel $B^{s}=|v-v_*|^{1-4s} b_s(\theta)$ with an angular singularity as $\theta\to 0$. Jang-Kepka-Nota-Vel\'azquez (2023) proved the limit $B^{s}\to…
We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d^2/dr^2+l(l+1)/r^2+w^2r^2+2g(r^2-a^2)/(r^2+a^2)^2, g>0. Two approaches are explored. A method for finding the quasi-polynomial solutions is presented, and…
We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in…
In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with Linac coherent light sources (LCLS) X-ray free electron laser (FEL) and Orion laser has been addressed. In both kind of…