相关论文: Solving Schrodinger Equation for Three-Electron Qu…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value…
A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis…
We investigate the dynamics of two interacting electrons confined to a pair of coupled quantum dots driven by an external AC field. By numerically integrating the two-electron Schroedinger equation in time, we find that for certain values…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction…
A review of some recently developed methods of calculating multiple differential cross-sections of photoionization and electron impactionization of atoms and molecules having two active electrons is presented. The methods imply original…
We consider the ADM splitting of the Einstein-Hilbert action in five dimensions in the presence of matter that can be either a "point particle", or a set of scalar fields. The Hamiltonian, being a linear superposition of constraints, is…
We present analytical solutions of the Schrodinger equation for the one-dimensional hydrogen molecular ion. In particular, we present closed form expressions for the electronic energy curves of this system that correspond to the ground…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
The two-dimensional electron-nuclear Schr\"odinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both…
We present a very efficient technique for solving the three-dimensional time-dependent Schrodinger equation. Our method is applicable to a wide range of problems where a fullly three-dimensional solution is required, i.e., to cases where no…
The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well…
The three-body Schr\"odinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with…
We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…