Related papers: Energy spectrum design and potential function engi…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, $\mathcal{F}(E)$, by writing in terms of confluent Heun functions. The…
Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…
We present the general form of potentials with two given energy levels $E_{1}$, $E_{2}$ and find corresponding wave functions. These entities are expressed in terms of one function $\xi (x)$ and one parameter $\Delta E=E_{2}$-$E_{1}$. We…
Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct…
We introduce a functional of the local spectral electron density which can be used to to compute the total energy and the local spectral function of strongly-correlated materials. We illustrate the applicability of the method by using as an…
Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
The adaptation rule for Vector Quantization algorithms, and consequently the convergence of the generated sequence, depends on the existence and properties of a function called the energy function, defined on a topological manifold. Our aim…
We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for…
We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…
In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of…
Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the…
The spectrum of a one-dimensional pseudospin-one Hamiltonian with a three-component potential is studied for two configurations: (i) all the potential components are constants over the whole coordinate space and (ii) the profile of some…
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland…
We calculate for the first time the static properties of the deuteron, within the framework of supersymmetric quantum mechanics, analytically. A new effective potential and its partner are derived from a superpotential so that all…