Related papers: Energy spectrum design and potential function engi…
We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We present SPARC-atomSFE, a spectral finite-element package for accurate and efficient atomic structure calculations within the framework of Kohn-Sham density functional theory. The package supports both all-electron and norm conserving…
We investigate the enlarged class of open finite strings in $(2+1)D$ space-time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple…
We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order (N$^3$LO) and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of…
This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with…
The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the…
We report on a methodology for the treatment of the Coulomb energy and potential in Kohn-Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We present a novel ab-initio single-electron approach to correlated electron dynamics in strong laser fields. By writing the electronic wavefunction as a product of a marginal one-electron wavefunction and a conditional wavefunction, we…
We consider a system of three particles, either three identical bosons or two identical fermions plus an impurity, within a three-dimensional isotropic trap interacting via a contact interaction. Using two approaches, one using an infinite…
In this paper, we present an approach for explicitly constructing quasi-periodic Schr\"odinger operators with Cantor spectrum with $C^k$ potential. Additionally, we provide polynomial asymptotics on the size of spectral gaps.
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schr\"odinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential,…
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and P\"oschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
We report on the recent progress on the computation of the doubly heavy baryon spectrum in effective field theory. The effective field theory is built upon the heavy-quark mass and adiabatic expansions. The potentials can be expressed as…
We analyze the application of the "tridiagonal representation approach" (TRA) to the Schr\"{o}dinger equation for some simple, exactly-solvable, quantum-mechanical models. In the case of the Kratzer-Fues potential the mathematical reasoning…
The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…
Motivated by recent progress on non-Hermitian topological band theories, we study the energy spectrum of a generic two-band non-Hermitian Hamiltonian. We prove rigorously that the complex energy spectrum of such a non-Hermitian Hamiltonian…
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills…