In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional elec...

As is widely-known, the eigen-functions of Landau problem in symmetric gauge are specified by two quantum numbers. The first familiar number $n$, whereas second magnetic $m$, which eigen-value canonical orbital angular momentum (OAM) operator electron. eigen-energies system depend only on and $m$ does not correspond to any direct observables. This seems natural since OAM generally believed be a...

mathematics or on quantum mechanics. List of All Articles 16 4.3 General Solution to Wave Equation Mukul Agrawal Noticing that f j t (t) forms an orthonormal set of functions, we get ( ∂ 2 ∂x2 + ∂ 2 ∂y2 + ∂ 2 ∂ z2 ) f j xyz(x,y,z) =−εμ0ωj f j xyz(x,y,z) (15) Hence the space dependent separable part of the eigen function of the operator i ∂ ∂ t , i.e. the f j xyz(x,y,z), should be an eigen funct...

In this paper, multi objective design of multi-machine Power System Stabilizers (PSSs) using Particle Swarm Optimization (PSO) is presented. The stabilizers are tuned to simultaneously shift the lightly damped and undammed electro-mechanical modes of all machines to a prescribed zone in the s-plane. A multi objective problem is formulated to optimize a composite set of objective functions compr...

We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on the eigen-decay of the kernel we provide a sharp characterization of the regr...

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0 D t u+ ∑d i=1 [cli aiD 2μi xi u+cri xiD 2μi bi u]+γ u = ∑d j=1 [κl j a jD 2ν j x j u+κr j x jD 2ν j b j u]+ f , where 2τ ∈ (0, 2), 2μi ∈ (0, 1) and 2ν j ∈ (1, 2), in a (1+d)-dimensional space-time hypercube, d = 1, 2, 3,...