Related papers: Role of the action function in defining electronic…
The expression of the electron broadening operator including the effect of penetrating collisions, i.e. for which the incoming electron enters the extent of bound-electron wavefunctions, is rather complicated, even for hydrogen. It involves…
The strong-interaction functionals $W_\infty[n]$ and ${W'}_\infty[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…
Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas…
We consider the extension of the standard single-determinant Kohn-Sham method to the case of a multiconfiguration trial wavefunction. By applying the rigorous Kohn-Sham method to this case, we construct the proper interacting and…
The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is…
We formulate the calculation of the ground-state wavefunction and energy of a system of strongly correlated electrons in terms of scattering matrices. A hierarchy of approximations is introduced which results in an incremental expansion of…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We consider a proposal to define the wave function of the Universe as a sum over spacetimes that eventually inflate. In the minisuperspace model, we explicitly show that a simple family of initial conditions, parametrized by a positive real…
Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic…
Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant.…
Electron-phonon ($e$-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons and metal-insulator transitions. First-principles approaches enable accurate…
It was recently shown that the exact potential driving the electron's dynamics in enhanced ionization of H$_2^+$ can have large contributions arising from dynamical electron-nuclear correlation, going beyond what any electrostatics-based…
In compound semiconductors and insulators, the polar electron-phonon coupling diverges at long range, known as the Fr\"ohlich interaction. Modern first-principles electron-phonon calculations treat the Fr\"ohlich interaction in a…
The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a…
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are…