Related papers: A simple and efficient numerical scheme to integra…
We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wavefunction) of the Schr\"odinger equation for a three-parameter short-range potential with 1/r, 1/r^2 and 1/r^3 singularities…
By using a simple procedure the general solution of the time-independent radial Schrodinger Equation for spherical symmetric potentials was made without making any approximation. The wave functions are always periodic. It appears two…
We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations…
In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schroedinger equation by…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
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…
Angular-momentum or parity-dependent nonlocal optical potentials for nucleon-${}^{16}\mathrm{O}$ scattering able to fit differential cross section data over the whole angular regime are developed and applied to the description of…
We perform two types of {\it ab initio} perturbation calculations of effective interactions in the Hartree--Fock (HF) basis instead of the harmonic-oscillator basis: one is called the Brillouin--Wigner (BW) perturbation and another is…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
The investigation delves into understanding how the Pauli exclusion principle influences the bare potential between atomic nuclei through the application of advanced theoretical methodologies. Specifically, the application of the novel…
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher…
In this paper, we consider nonlocal Schr\"odinger equations with certain potentials $V$ given by an integro-differential operator $L_K$ as follows; \begin{equation*}L_K u+V u=f\,\,\text{ in $\BR^n$ }\end{equation*} where $V\in\rh^q$ for…
Background: The effects of non-local potentials have historically been approximately included by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as…
A study of the nucleon mean-field potential in nuclear matter (NM) is done within an extended Hartree-Fock (HF) formalism, using the CDM3Y6 density dependent version of the M3Y interaction which is associated with the nuclear…
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded,…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…
We write a computer program that uses the recursion relation to calculate wave function in the harmonic-oscillator potential for specified values of E/hv (with its deviation 0.001) containing only even numbers of v (0,2,4,...). In this…
The inverse scattering theory for many-body systems in quantum mechanics is an important and difficult issue not only in physics---atomic physics, molecular physics and nuclear physics---but also mathematics. The major purpose in this paper…