Related papers: Singular Short Range Potentials in the J-Matrix Ap…
Recently, we proposed an exact method for direct calculation of the Jost function for central potentials (which may have Coulombic tails) and the Jost matrix for non-central short range potentials. This method works for all real or complex…
The J-matrix method of scattering is used to obtain analytic expressions for the phase shift of two classes of relativistic exponential-type separable potentials whose radial component is either of the general form r^(n-1)exp(-r) or…
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…
Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb ($-A/r$) and the Yukawa ($Be^{-Cr}/r$) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to…
Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…
This work presents an alternative methodology for computing potentials matrix elements within the Lagrange-mesh method in momentum space. The proposed approach extends the range of treatable potentials to include previously inaccessible…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
The problems of matrix spectral factorization and J-spectral factorization appear to be important for practical use in many MIMO control systems. We propose a numerical algorithm for J-spectral factorization which extends Janashia-Lagvilava…
The paper proposes a hybrid method for calculating scattering processes that combines the $J$-matrix method with exterior complex scaling as an absorbing boundary condition. It represents the wave function as a finite sum of oscillator…
The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional…
The spherical-box approach is extended to calculate the resonance parameters and the real part of the wave function for single particle resonances in a potential containing the long-range Coulomb interaction. A model potential is taken to…
We study an integrable quantum field theory of a single stable particle with an infinite number of resonance states. The exact $S$--matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles…
A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method…
The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet $^1S$ and triplet $^3S+^3D$ channels. The complete Hilbert space is split into two domains, the model subspace $S_0$, in which the two-particle propagator is…
This paper presents an accurate highly efficient method for solving the bound states in the one-dimensional Schr\"odinger equation with an arbitrary potential. We show that the bound state energies of a general potential well can be…
We show that a quantum system with nonlocal interaction can have bound states of unusual type -- Isolated States (IS). IS is a bound state that is not in correspondence with the $S$-matrix pole. IS can have a positive as well as a negative…
The generalized pseudospectral method is employed to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulth\'en potential. In both instances, arbitrary…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb…
We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate…