Effect of ordering ambiguity in constructing the Schrödinger equation on perturbation theory

This work explores the application of perturbation formalism, developed for isotropic velocity-dependent potentials, to three-dimensional Schr?dinger equations obtained using different orderings of the Hamiltonian. It is found that the formalism is applicable to Schr?dinger equations corresponding to three possible ordering ambiguities. The validity of the derived expressions is verified by considering examples admitting exact solutions. The perturbative results agree quite well with the exactly obtained ones.     

Cross-ladder effects in Bethe-Salpeter and light-front equations

The Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding light-front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches --BS and LF-- give very close results.     

Spectra of baryons containing two heavy quarks

Doubly heavy baryons, i.e., the baryons containing two heavy quarks are treated in the adiabatic approximation, considering the motion of the light quark as a relativistic motion. The binding energy and mass spectra of doubly heavy baryons are calculated solving the two-center Dirac equation the one-centre Schr?dinger equation for Coulomb plus linear potential. The binding energy of the light quark as a function of the distance between heavy quarks is found. Received: 16 January 2002 / Accepted: 7 February 2002     

Numerical outflow boundary conditions for the shallow-water equations

A simple explanation is given of the occurrence of wiggles in the flow field near outflow boundaries. If the shallow-water equations are solved numerically spurious solutions with an oscillatory character turn out to exist, which can be generated by certain additional numerical boundary conditions on the downstream side. The wiggles usually damp quickly with the distance from the boundary. Some ways of handling the downstream boundary are given which largely avoid the occurrence of wiggles.     

l-solutions and stability analysis of difference equations using the Kummer’s test

We address the p-summability and asymptotic stability properties in nonautonomous linear difference equations. We focus our discussion on two kind of difference equations. The first one is a first order system of linear nonautonomous difference equations, and our discussion involves the use of Kummer’s convergence test. The second one is a linear nonautonomous scalar higher order difference equation. In this case our discussion is based on a recently introduced transformation of a higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. We give insight on our ideas that are behind our methods, prove new results, and show applications.     

Infinite Systems of Quasilinear Differential Difference Inequalities and Applications

The article deals with the initial boundary value problem for an infinite system of first order quasilinear functional differential equations. A comparison result concerning infinite systems of differential difference inequalities is proved. A function satisfying such inequalities is estimated by a solution of a suitable Cauchy problem for an ordinary functional differential system. The comparison result is used in an existence theorem and in the investigation of the stability of the numerical method of lines for the original problem. A theorem on the error estimate of the method is given. The infinite system of first order functional differential equations contains, as particular cases, equations with a deviated argument and integral differential equations of the Volterra type.     

Curves of Positive Solutions for Supercritical Problems

For the Dirichlet problem on ball in R n with p < ( n + s )/( n m 2), we show existence of a critical u 0 > 0, such that there are two positive radial solutions for u ] (0, u 0 ), one at u = u 0 , and none for u > u 0 . In another direction we show that for the model problem with 1 h q < ( n + 2)/( n m 2) < p , on a bounded star-shaped domain in R n , there is a u * > 0 so that the problem has no positive solution for u < u *.     

On the Diffraction by Biperiodic Anisotropic Structures

This article studies the scattering of electromagnetic waves by a nonmagnetic biperiodic structure. The structure consists of anisotropic optical materials and separates two regions with constant dielectric coefficients. The time harmonic Maxwell equations are transformed to an equivalent strongly elliptic variational problem for the magnetic field in a bounded biperiodic cell with nonlocal boundary conditions. This guarantees the existence of quasiperiodic magnetic fields in H 1 and electric fields in H (curl) solving Maxwell's equations. The uniqueness is proved for all frequencies excluding possibly a discrete set. The analytic dependence of these solutions on frequency and incident angles is studied.     

Existence of multiple positive solutions for fourth order two-point boundary value problems

The present article tackles two-point boundary value problems for fourth-order differential equations as follows <artwork name="GAPA31044eu1"> Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.     

On the Relative Intensity-Concentration Relationship of Carbonyl Bands in the Solution Infrared Spectra of Metal Carbonyl Compounds of C4v Symmetry

The theory on the relative intensities of CO stretching bands of metal carbonyl compounds of C^4v symmetry has been advanced by orgel, inter alios. ² For complexes of formula M(CO)₅Xⁿ [a = -1, 0), three infrared active bands are expected, 2A₁ + E. The two A₁ bands consist of modes which are predominantly vibration of the CO trans to X (A₁ ⁽¹⁾) and the symmetrical stretch of the four equatorial CO's (A^{1 (2)}). The A₁ ⁽²⁾ band is nearly forbidden, and owes its intensity to the contribution of the axial CO stretch to the normal mode. The end result of this coupling between axial and radial CO stretching symmetry modes would appear to be an aid in assigning the bands in the carbonyl stretching region to the appropriate symmetry modes; the relative intensities are weak (A₁ ⁽²⁾), strong (E), and medium (A₁ ⁽¹⁾) Although this weak-strong-medium pattern is invariably observed in the spectra of