In this work, we study the wavefunctions of the one dimensional 1/r Hubbard model in the strong interaction limit U = ∞. A set of Gutzwiller-Jastorw wavefunctions are shown to be eigen-functions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wavefunctions. For the wavefunctions and integrability conditions at finit...

Abstract The polynomial solution of the Schrödinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By using a pr...

The impact of the latest combined CHAMP/GRACE/terrestrial measurements Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some linear combinations of the nodes of some of the existing Earth’s artificial satellites is presented. The 1-sigma upper bound of the systematic error in the nodenode LAGEOS-LAGEOS II combination is 3.9% (4% with EIGENGRACE02S, ∼ 6% with ...

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fract...

A modeling study on the energy absorption and heat transfer of concentric nanoparticles under localized surface plasma resonance (SPR) conditions is presented. A generalized theoretical formulation for multi-scattering of electromagnetic waves by multilayered nanoparticle is employed to determine the heat source first, and then starting with the Eigen functions, direct and inverse integral tran...

The global electrostatic mode in pair-ion plasmas is discussed for cylindric geometry and for a radially inhomogeneous equilibrium density. In the case of a Gaussian radial density profile, exact analytical eigen solutions are found in terms of the Kummer confluent hypergeometric functions. The mode is identified as a convective cell propagating in the poloidal and axial direction, having at th...

Using a Hamilton-Jacobi equation approach, we obtain analytic equations for steady-state population distributions and mean fitness functions for Crow-Kimura and Eigen-type diploid biological evolution models with general smooth hypergeometric fitness landscapes. Our numerical solutions of diploid biological evolution models confirm the analytic equations obtained. We also study the parallel dip...

We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures justifying their use as shape functio...