相关论文: The Classical Schrodinger's Equation

The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…

In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…

The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…

Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…

We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…

The time-dependent Schr\"odinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the…

We consider the spectrum of the discrete Schr\"odinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of absence of singular part of the spectrum. We calculated also…

Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…

A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the…

Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…

Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are…

Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On one hand, such an equation generalizes the traditional Schrodinger-Newton and…

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a…

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…

The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…

This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper…

A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…

We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…