Related papers: Wronskian method for bound states
In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for…
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…
A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We obtain eigenvalues and eigenfunctions of the Schr\"{o}dinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical…
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
The Schrodinger equation for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states energies. Additionally, the corresponding wave functions are expressed by the Jacobi polynomials. The…
We discuss a recently proposed analytical formula for the eigenvalues of the Gaussian well and compare it with the analytical expression provided by the variational method with the simplest trial function. The latter yields considerably…
We apply a stochastic method of minimizing the ground state energy in variational calculations of light nuclei using the Refined Resonating Group Model (RRGM). The method utilizes a bit representation of the width parameters to be varied.…
It is considered that the effective interaction between any two quarks in a baryon can be approximately described by a simple harmonic potential. Also, it is made use of the nonrelativistic approximation. The problem is firstly solved in…
We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the…
Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
This talk reviews several aspects of the "semirelativistic" description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
By using the Pekeris approximation, the Schrodinger equation is approximately solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method. The energy levels are worked out and the…