Series Of Wave Functions Research Articles

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression with Taylor's series. The transmitted field in the homogeneous gyrotropic cylinder is expressed in terms of the series of wave functions based on the integral equation. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions of continuous tangential electric and magnetic fields. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

A Green Function of Vertical Interfacial Point Source SH Wave Scattering by a Circular Lining in an Elastic Quarter Space

An anti-plane Green function is formulated for steady state solution of a circular lining impacted by a vertical interfacial point source in an elastic quarter space. Series forms of scattering and stationary wave of the circular lining are constructed with Fourier wave function expansion method. Basic solution of the anti-plane point source is employed to represent displacement fields of incident wave. Stress-free conditions on the quarter bounds are satisfied by using image method. Displacement and stress continuity conditions of the lining are expanded as Fourier series to determine definite equations of unknown coefficients of wave function series.

TE-wave scattering from a shallow circular channel in a perfectly conducting plane

The problem of TE-wave scattering by a shallow circular channel in a perfectly conducting plane is considered and its rigorous series solution is also derived. By the region-matching technique, a semi-circular auxiliary boundary is introduced to divide the analyzed region into two subregions. The magnetic field of each subregion is represented in terms of an infinite series of wavefunctions with unknown coefficients. To include more practical applications, the wave source is assumed to be a Gaussian beam. The Kozaki's approximate expansion for Gaussian-beam incidence is adopted, which can convert into the plane-wave expansion with a special condition. With the enforcement of interface continuity conditions and the satisfaction of the channel surface boundary condition through the Graf's addition formula, the unknown expansion coefficients are determined. Comparisons for the semi-circular channel case with available data in the literature indicate excellent agreement. Pronounced effects of the depth-to-half-width ratio of the channel on backscattering width, far-field radiation pattern and equi-amplitude distribution of the magnetic field are illustrated by graphical results. The flexible and tunable features of the presented geometry make it easily applicable to the design and fabrication of multiple finite channels for optical devices.

Electromagnetic Wave Scattering by Elliptic Chiral Cylinder

An exact boundary value solution for the scattering of transverse magnetic (TM) wave by an elliptic chiral cylinder is developed and presented in this paper. The solution is based on the separation of variable technique in the elliptic cylinder coordinates system and expressed in terms of Mathieu and modified Mathieu functions. The incident, transmitted and scattered electromagnetic waves are expressed in terms of infinite series of wave functions. The matrix form of the expansion coefficients is found by applying the boundary conditions and orthogonality of the Mathieu functions. Numerical results of the forward and back scattered echo widths for co- and cross-polarized waves with TM and TE polarized incident fields, for various cases are presented and discussed.

Quantum Analysis of Hole Distribution in Multiple-Delta-Doped Diamond with a Deep Impurity Level

Multiple-delta-doping (MDD) in synthetic diamond films is studied analytically from the quantum-mechanical point of view by solving Schroedinger's and Poisson's equations simultaneously and self-consistently. From the analysis, a series of wave functions and subbands are determined, and more accurate distribution of holes than from the classical-mechanical point of view is obtained. In MDD diamond films at 500 K, in spite of the deep impurity level, hole excitation efficiency rises to 4–5 times that of uniformly doped films. Moreover, 95% of holes are located in the nondoped layer where the mobility is high. These two beneficial features of MDD markedly improve the conductance as compared with that of uniformly doped diamond films.

Properties of wave functions in homogeneous anisotropic media.

The general solutions of the first, second, third, and fourth kinds to the wave equation in homogeneous anisotropic media are expressed by integrals over a finite range. The convergence of the series solution of wave functions in homogeneous anisotropic media [Phys. Rev. E 47, 664 (1993)] is discussed. The use of the wave functions in anisotropic media is demonstrated. The theory is expounded via an illustrative example of a two-dimensional scalar case. The analytical solution of plane-wave scattering by a conducting circular cylinder coated with anisotropic materials is formulated in terms of the series of wave functions for anisotropic media. Numerical results show that the solution in terms of wave functions of various kinds in anisotropic media gives essentially the same radar cross sections as obtained by Beker, Umashankar, and Taflove [Electromagnetics 10, 387 (1990)] using a different approach. Numerical results in the resonance region are presented for reference purposes. The analysis of this paper can be easily generalized to vector and tensor wave functions in homogeneous anisotropic media.

Axial slot antenna on an anisotropic dielectric-coated circular cylinder

This paper presents an analytical solution of an axial slot antenna on a conducting circular cylinder coated with an anisotropic material in terms of the series of wave functions for anisotropic media. This solution is formally similar to the solution of an axial slot antenna on a conducting elliptic cylinder with an isotropic dielectric coating. In the anisotropic dielectric coating, and in the exterior free space region, the fields are expanded by the wave functions in anisotropic media and the well known wave functions in isotropic media, respectively. Numerical results for the far-field radiation patterns and the aperture conductance against coating thickness for different anisotropic media are presented for the transverse electric (TE) and transverse magnetic (TM) polarisations. Numerical results for the gyrotropic type media are used to check our calculations, and those for general anisotropic media are presented to provide references for future computations by using other methods, respectively.

Scattering of plane sh waves by a semi‐cylindrical hill

AbstractA new analytical method is presented to study the problem of scattering of plane SH waves by a semi‐cylindrical hill in an otherwise homogeneous, isotropic and elastic two‐dimensional half‐space, using the series of wave functions and a new expansion technique. The results obtained show that (1) the hill has quite considerable effects on ground motions for both the points on the hill and its environs, (2) these effects depend mainly on the frequency, the angle of wave incidence and the ratio of radius of hill to one‐half the wave length of incident waves, and (3) prominent and depression topographies having equal form and radius for the same incident waves would cause quite different mechanisms of wave propagation in both response performance and magnitude. The results, doubtless, would be useful for further deepening knowledge of the effects of prominent topography on seismic ground motion and for testing the accuracy of various approximate methods so far available.

Higher orders of semiclassical expansion for the one-dimensional Schrödinger equation.

The divergence of a semiclassical series of wave functions due to the presence of one or two turning points is investigated. The asymptotic expansion of higher semiclassical corrections ${\ensuremath{\varphi}}_{n}$ with respect to the inverse power of the order number n is obtained. Amazingly, the expansion terms are subject to the same recurrence relations as the terms of the initial expansion with respect to Planck's constant \ensuremath{\Elzxh}. Quantitative criteria for obtaining maximally accurate semiclassical wave functions are derived.

The influence of electron correlation on generalized oscillator strengths for He

The excitation transitions considered are 11S to 21P and 11S to 31P. Electron correlation is introduced into the description of the 11S ground state in a systematic way by using the natural expansion of a configuration-interaction (CI) wavefunction developed by Weiss. By truncating this expansion to the first X terms and renormalizing a series of wavefunctions ranging from a Hartree-Fock equivalent (X=1) to the full CI function (X=15) are obtained. Operating within the first Born approximation, three standard formulations for evaluating f(K) are used and their sensitivity with respect to correlation effects is discussed and a comparison of the present results is made with those of other workers. Although the inclusion of the first correlation configuration in the 11S wavefunction did not necessarily guarantee an improvement in f(K), the introduction of the second correlation term in the natural expansion gave rise to a significant improvement in f(K) for all K regardless of the mode of calculation.

Near-Hartree-Fock assessment of reorganization effects in ionic states of acetylene

Calculations on acetylene 2Πu and 2Πg ions and the 1Σg neutral ground state using a series of wavefunctions with increasing basis set size converge to an estimated Hartree-Fock vertical ionization energy near 10.0 eV and an estimated Hartree-Fock vertical electron affinity near −4.2 eV. The calculations reveal that the near-Hartree-Fock σ orbitals change strongly with the state of ionization leading to σ-electron energy errors (for transferring ground state σ orbitals to the ions) of − 4.5 eV for the cation and + 3.2 eV for the anion. Each carbon atom is calculated to lose only about 0.34 e upon π-electron ionization and to gain about 0.42 e on π-electron capture. Consequently there is poor transferability of the ground state HF σ core to the ionic states so that π-electron energy changes of + 3.2 eV for the cation and − 3.8 eV for the anion are incurred. The error incurred by transferring π orbitals from the ground state to the ions with frozen σ core is −0.8 eV for the cation and − 0.35 eV for the anion. The σ- and π-orbital reorganization effects largely cancel on going to the ions producing gross reorganization energy changes of − 1.3 eV in the cation and − 0.55 eV in the anion. Comparison with C(sp2)→C+ and ethylene π-electron ionization indicate that aside from extensive σ-π cancellation reorganization effects are not transferable between these species. At least double zeta level basis sets are necessary for physically meaningful descriptions of ionic processes.

A comparison of the resonance, perfect pairing, and molecular orbital wavefunctions for BeH2

Series of wavefunctions for the ground state of BeH2 have been compared in the frameworks of the valence bond and the molecular orbital theories for Be-H distances between 1·5 a.u. and 6·0 a.u. using minimum basis sets of Slater-type orbitals with exponents optimized at each internuclear distance. It is confirmed that the model based on the resonance valence state can be useful, particularly when ionic configurations are incorporated with it, although the model emphasizing perfect pairing and including an additional parameter to determine ionic character provides significantly the lowest energies for cases where there is a single degree of freedom in the mixing of valence bond structures. Both molecular orbital and valence bond calculations indicate it is a very good approximation to consider BeH2 as involving localized electron-pair bonds.

Conditions of analogy between the propagation of electromagnetic waves and the trajectories of particles of same spin with application to rectifying magnetrons

The object of this article is the study of the biunivocal correspondence established by the Pauli principle between the internal energy of a particle and the frequency of the associated wave in media which are the seat of strong coupling between the particles and when their spins are in a favored direction. In Section I, the determinantal forms of antisymmetrical wave functions are investigated, these being valid both for crystals and for electronic plasmas. It is shown that, starting from this determinant, two complementary series of wave functions can be constructed. Depending on the internal energy, two types of complementary particles are thus obtained: (1) free electrons associated with real waves, and (2) holes associated with evanescent waves. In Section II, a study is made of the mathematical analogy between the Schrodinger equation and the tropospheric propagation equation. It is shown that the potential energy can be assimilated to the refraction modulus and that the group velocity of the propagation around the earth can be assimilated to the group velocity of the complementary particle. By a very simple correspondence, the real modes of propagation predict the formation of holes while the imaginary modes of propagation predict the formation of free electrons. A special study is made of the analogy between the index barriers of the inversion layers and the potential barriers of the barrier layers. This analogy enables the existence to be predicted of purely electronic barrier layers without the need for any material support. In Section III, the rectification and photoconduction properties of these electronic barrier layers in magnetrons and in traveling wave magnetron detectors are considered. Their analogies with and differences from the barrier layers of p-n junctions are examined. Finally, in the conclusion, the advantages and description of radar detection arrangements devised, on these principles, by the Compagnie Generale de T.S.F. in Paris, are set out.