Related papers: Pre-Born-Oppenheimer Dirac-Coulomb-Breit computati…
The motion of a muon in two centers coulomb field is one of the interesting problems of quantum mechanics. The adiabatic expansion method is powerful approach to study the muonic three-body system. In this investigation the three-body…
The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present…
In the heavy quark limit, a doubly heavy baryon is regarded as composed of a heavy diquark and a light quark. We establish the Bethe-Salpeter (BS) equations for the heavy diquarks and the doubly heavy baryons, respectively, to leading order…
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic…
We revive an approach to solve the Dirac equation originally proposed by Kutzelnigg which makes use of the squared Dirac operator $\hat{\mathfrak{D}}^{2}$. This approach holds the promise to avoid the negative energy solution because the…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincar\'e symmetry,…
Structure and properties of families of critical points for classes of functions $W(z,\bar{z})$ obeying the elliptic Euler-Poisson-Darboux equation $E(1/2,1/2)$ are studied. General variational and differential equations governing the…
The energies and wave functions of the two-body Dirac equation for positronium are compared with those of the Pauli approximation and the Bethe-Salpeter equation. The unusual behavior of the ground-state wave function of the Dirac equation…
For solving the $2\to 2,3$ three-body Coulomb scattering problem the Faddeev-Merkuriev integral equations in discrete Hilbert-space basis representation are considered. It is shown that as far as scattering amplitudes are considered the…
We derive covariant equations describing the three-quark bound state in terms of quark and diquark degrees of freedom. The equations are exact in the approximation where three-body forces are neglected. A feature of these equations is that…
Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We discuss a 1D many-body model of distinguishable particles with local, momentum dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
Positron binding energies and Dyson orbitals for five-membered heterocycles with N, O, S and NH substituents are predicted \emph{ab initio} via many-body theory. The positron-molecule correlation potential (self energy) is calculated via…
The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We…
We derive the Dirac equation for a particle in the background of the Newman-Unti-Tamburino (NUT) spacetime by applying the tetrad formalism, and separate the angular and radial parts. We get the system of two differential equations for…
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The…
We lay out the extension of range-separated density-functional theory to a four-component relativistic frame-work using a Dirac-Coulomb-Breit Hamiltonian in the no-pair approximation. This formalism combines a wave-function method for the…