Related papers: Cornell Potential: A Neural Network Approach
The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…
We demonstrate the utility of physics-informed neural networks (PINNs) as solvers for the non-relativistic, time-dependent Schr\"odinger equation. We study the performance and generalisability of PINN solvers on the time evolution of a…
The four exactly-solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials,…
The Hellmann potential is a superposition potential that consists of an attractive Coulomb potential and a Yukawa potential. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have studied the approximate analytical…
In a recent paper by Barton (J. Phys. A40, 1011 (2007)), the 1-dimensional Klein-Gordon equation was solved analytically for the non-singular Coulomb-like potential V_1(|x|) = -\alpha/(|x|+a). In the present paper, these results are…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential $V$. The main concern is treating nonlinearities whose degree is low…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
A set of quasi-exactly solvable quantum mechanical potentials associated with the Poeschl-Teller potential, the generalized Poeschl-Teller potential, the Scarf potential, and the harmonic oscillator potential have been studied. Solutions of…
Phenomenological potentials describe the quarkonium systems like Charmonia, Bottomonia and $B_c$ Meson. They give a good accuracy for the mass spectra. In the present work we extend one of our previous works in the central case by adding…
The exact Dirac equation for the energy-dependent Coulomb (EDC) potential including a Coulomb-like tensor (CLT) potential has been studied in the presence of spin and pseudospin (p-spin) symmetries with arbitrary spin-orbit quantum number…
We consider the following system of Schr\"odinger equations \begin{equation*}\left.\begin{cases} -\Delta U + \lambda U = \alpha_0 U^3+ \beta UV^2 -\Delta V + \mu(y) V = \alpha_1 V^3+\beta U^2V \end{cases}\right. \text{in} \quad…
We develop a new method for solving two- and three-body bound state problems using unsupervised machine learning techniques. We use a deep neural network to calculate both simple and realistic potentials, obtaining the properties of the…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
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 have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic…
This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without…