We have recently presented a method for solving the time-dependent Schrodinger equation by collocation on various members of a family of spatial grids and have shown that this method is interpretable in terms of the expansion of the wave function in a basis of discrete coordinate eigenfunctions. The method is applicable to molecular systems with one or multiple spatial dimensions, and also to b...

In this paper, we model a microtubule based on its dimer resolution structure. First, the fundamental structural components were studied and then electrostatic potential function for a single monomer was calculated. Subsequently, the potential function inside a single monomer due to a ring of dimers was obtained. Considering the potential due to protofilament-protofilament interaction with a mo...

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the dr...

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger ...

In order to solve nonlinear kinetic equations for recombination reactions when the production of participating species is driven externally at a time-dependent rate, we establish a framework based on the correspondence between these equations and a Schrodinger-type equation in which the product of the recombination constant with the production rate plays the role of the potential. The required ...

A method of connecting the Korteweg~e Vries (KdV) equation, known from the theory of nonlinear waves, with the SchrOdinger equation was discovered in 1967,Pl This method is applied in the present paper to a study of a periodic problem. We find exact analytical formulae for a class of solutions u (x ,t) such that at any moment in time t the potential u (x ,t) of the Schrodinger operator has only...

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori wh...

Gaussons: Solitons of the logarithmic Schrodinger equation. Iwo Bialynicki-Birula (Institute of Theoretical Physics, Warsaw University, Warsaw, Poland and Department of Physics, University of Pittsburgh, Pittsburgh, U.S.A.); and J erzy Mycielski (Institute of Theoretical Physics, Warsaw University, Warsaw, Poland). Physica Scripta (Sweden) 20,539-544,1979. Properties of the Schrodinger equation...

We derive the amplitude equation, in the weakly nonlinear regime, for an optical wave packet that propagates in an initially undistorted nematic liquid crystal. By using the dyad representation Q i j , we find the retarded and nonlocal equation for the nematic configuration and solve it in Fourier space. This allows us to calculate the amplitude dependent dispersion relation for a nematic liqui...

In this paper, we primarily explore numerical solutions to the Quantum 1D Infinite Square Well problem, and the 1D Quantum Scattering problem. We use different finite difference schemes to approximate the second derivative in the 1D Schrodinger’s Equation and linearize the problem. By doing so, we convert the Infinite Well problem to a simple Eigenvalue problem and the Scattering problem to a s...