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1.
A simple and straightforward calculating scheme is suggested for finding wave functions
of the hydrogen atom in prolate spheroidal coordinates. The wave functions are found in an
explicit form by the direct solution of appropriate one-dimensional equations. The
suggested calculating scheme allows us to carry out simple calculations and to obtain
spheroidal wave functions in principle for arbitrary eigenstates of the hydrogen atom.
Expansions are found for the obtained spheroidal wave functions over a spherical basis. 相似文献
2.
Xiao-ou Cai 《Optik》2013
In accordance with the theory of partially coherent light, the correlation degree of light disturbance for all pairs of object points has been expounded and measured with their mutual intensity. Furthermore, the expression of mutual intensity distribution on the image plane by a set of prolate spheroidal wave functions has been given. Then, the number of freedom degree of light field on the image plane has been worked out illuminated by three light conditions, coherent, incoherent and partially coherent light. This approach provides a novel expression of 3D display information. 相似文献
3.
A. B. Maizel’ 《Acoustical Physics》2004,50(6):717-720
Using the theory of spheroidal wave functions, the total acoustic impedance is determined for a prolate spheroid performing transverse translational and rotational oscillatory movements. Expressions for the radiation resistance, the added mass, and the added moment of inertia are derived. It is shown that, in the lowfrequency approximation, this mass and moment of inertia reach limiting values identical to hydrodynamic ones. The components of the total acoustic impedance are calculated for spheroids of different relative thicknesses at an arbitrary frequency. 相似文献
4.
Touvia Miloh 《Acoustical Physics》2016,62(6):663-671
A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an “ultimate” singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave. 相似文献
5.
An approach to express an incident shaped beam with respect to an arbitrarily oriented spheroidal particle having layers with non-confocal boundaries is presented. To overcome the difficulty of non-confocal boundary conditions connected with different spheroidal coordinate systems, a theoretical procedure is developed to deal with the non-confocal boundary conditions by virtue of a transformation for vector wave functions. The unknown coefficients of scattered and internal electromagnetic fields are determined by solving a system of linear equations derived from the boundary conditions and relations between the spheroidal vector wave functions and spherical ones. Numerical results of the normalized scattering cross section for a two-layered non-confocal prolate spheroid are evaluated. PACS 42.25.Fx; 42.25.Bs 相似文献
6.
In the present contribution we compare the new Multitaper Filtering technique with the very popular Filter Diagonalization Method. The substitution of a time-independent problem, like the standard Schrödinger equation, by a time-dependent one from the Filter Diagonalization Method allows the employment of and comparison with standard signal processing filtration machinery. The use of zero-order prolate spheroidal tapers as filtering functions is here extended and exactly formulated using techniques originating from general investigations of prolate spheroidal wave functions. We investigate the modifications presented with respect to accuracy and general effectiveness. The approach may be useful in various branches of physics and engineering sciences including signal processing applications as well as possibly also in general time-dependent processes. 相似文献
7.
Coulomb Sturmians are obtained in prolate spheroidal coordinates by separation of variables in the Schrödinger equation and direct solution of the appropriate one-dimensional equations. Molecular orbitals are expressed as linear combinations of the introduced Coulomb Sturmians and some low-lying energy terms and corresponding wave functions are calculated for one-electron diatomic molecules. It is shown that similarity of the one- and two-centre orbitals in spheroidal coordinates, combined with completeness and good convergence properties of Coulomb Sturmians, substantially speeds up convergence and makes the calculated results closer to the exact ones. Application of the elaborated calculating scheme for diatomic many-electron molecules is discussed. 相似文献
8.
Kuznetsova LA Khanna S Amso NN Coakley WT Doinikov AA 《The Journal of the Acoustical Society of America》2005,118(1):104-112
The self- and mutual radiation impedances and the farfield directional response of rectangular pistons conformal to a rigid elliptic cylindrical baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution for the acoustic pressure is expressed in terms of a modal series representation in Mathieu functions. The Mathieu functions are obtained using computer programs that have been recently developed to provide accurate values of the functions at high frequencies. Results for the normalized self- and mutual radiation resistance and reactance and the directional response of acoustic radiation are presented over a wide frequency range for different piston sizes and elliptic cylinder cross section shapes. 相似文献
9.
V. G. Farafonov 《Optics and Spectroscopy》2013,114(3):421-431
We have constructed a solution to the problem of scattering by a nonconfocal multilayer particle. The main difficulty was to join expansions constructed in two spheroidal systems on either side of each boundary. As a result of a detailed consideration of relations between scalar wave spheroidal and spherical functions, we have succeeded in finding a representation of the former in terms of the latter and vice versa. In the final form, the joining of solutions is described by only one matrix, which depends on coefficients of representations of angle spheroidal functions in terms of associated Legendre functions of the first kind. Since the problem has been solved using an approach that involves the method of extended boundary conditions, the dimension of the system for numerical determining unknown coefficients is equal to the number of terms that are taken into account in field expansions and does not depend on the number of particle layers. Previously performed numerical calculations for confocal particles have shown a very high efficiency of the algorithm not only for particles that are close to spheres in shape, but also for strongly prolate and strongly oblate spheroids. In addition, the algorithm makes it possible to calculate optical properties of particles that have dozens of layers. 相似文献
10.
在工业上和在实验室中,我们都会遇到两个物体之间的电磁屏蔽的问题。在许多应用中,我们只须注意到两个物体之间的静电屏蔽就够了,因而它们之间的相互作用可以从计算它们之间的相互电容来定出。当干扰物体的尺寸很小因而可以认为是一个点电源时,则当它与另一个接地导体(即问题中的电磁屏蔽)共同存在时所生的效应即可由这一个接地导体的格林函数表出。关于格林函数的知识已有很丰富的积累,因而本文中所提出的方法是可以解决多种多样的问题的。文中讨论了扁椭球坐标和长椭球坐标中的格林函数,并对带虚数自变数的勒讓特函数的若干个公式作了推导,因为这些有用的公式在流行的文献中还未见到。导体表面任意形状的小孔的问题是值得讨论的,特别是有限大导体表面上的小孔问题,本文从理论上验证了文献上已经提出来的实验结果。最后我们给出如下两个物体之间的相互电容公式:其中一个是在带小孔的闭合电磁屏蔽体的另一个之内。 相似文献
11.
A phase shift formulation of scattering by oblate and prolate spheroids is presented, in parallel with the partial-wave theory of scattering by spherical obstacles. The crucial step is application of a finite Legendre transform to the Helmholtz equation in spheroidal coordinates. In the long-wavelength limit the spheroidal analog of the spherical scattering length immediately gives the cross section. Analytical results are readily obtained for scattering of Schro?dinger particle waves by impenetrable spheroids, and for scattering of sound waves by acoustically soft spheroidal objects. The method is restricted to scattering by spheroids whose symmetry axis is coincident with the direction of the incident plane wave. 相似文献
12.
We construct and study an analytical solution of the boundary-value problem for the radiation field of a small spheroidal
antenna located in free space and surrounded by a thin shell of cold homogeneous isotropic plasma. Conditions for a resonant
increase in the field in free space as a function of the plasma-shell thickness with the variation in the spheroidal-antenna
shape are studied. It is shown that the plasma shell has the largest effect on the radiation field of a strongly prolate spheroidal
antenna.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 246–257, March 2006. 相似文献
13.
The problem of light scattering by nonspherical particles, which arises in many applications, is nowadays most frequently solved by the method of extended boundary conditions in combination with the expansion of the fields in terms of spherical wave functions. However, such an approach encounters difficulties if the shape of particles is far from spherically symmetric, even in the simplest case of spheroids with the semiaxis ratio a/b > 5?10. A new approach to solving this problem is proposed, which also applies the extended boundary condition method but involves the expansion of the fields in terms of spheroidal functions. In this case, to obtain effective solutions for strongly prolate and oblate particles, the fields are divided in two parts with known properties and specific scalar potentials are used for each part. The basic relations of the approach are presented and some results of calculations of the optical properties of spheroids and spheroidal Chebyshev particles that are performed using computer codes realizing this approach are given. The convergence of the results for different cases and the domain of applicability of the method are discussed. 相似文献
14.
Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field 总被引:1,自引:0,他引:1
Barton JP Wolff NL Zhang H Tarawneh C 《The Journal of the Acoustical Society of America》2003,113(3):1216-1222
A general spheroidal coordinate separation-of-variables solution is developed for the determination of the acoustic pressure distribution near the surface of a rigid spheroid for a monofrequency incident acoustic field of arbitrary character. Calculations are presented, for both the prolate and oblate geometries, demonstrating the effects of incident field orientation and character (plane-wave, spherical wave, cylindrical wave, and focused beam) on the resultant acoustic pressure distribution. 相似文献
15.
D. A. Baghdasaryan D. B. Hayrapetyan E. M. Kazaryan 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2016,51(2):157-161
In a uniformly charged prolate spheroidal Thomson hydrogen atom the electron states have been investigated. It has been shown from the mathematical point of view that the problem is equivalent to a spheroidal hydrogen atom in a parabolic potential with the cylindrical symmetry. In the framework of adiabatic approximation, the energy of ground state has been calculated. Comparison with the case of uncharged spheroidal quantum dot has been made, and the analytical form of wave function of electron has been also obtained. 相似文献
16.
The converging prolate spheroidal functions are introduced. They are shown to exhibit phase conjugacy properties under both finite and infinite Fresnel transformation. Their use in Fresnel optics is illustrated. In particular, the number of degrees of freedom of a Fresnel diffracted field is evaluated. 相似文献
17.
Tamaz Kereselidze George Chkadua Pierre Defrance J. F. Ogilvie 《Molecular physics》2013,111(1):148-161
Coulomb Sturmian amplitude functions are derived in prolate spheroidal coordinates and are presented in a closed algebraic form. Spheroidal Sturnian functions are revealed to be related to the polynomial solutions of Heun's confluent equation. A reduction of symmetry from spherical to axial leads to the coupling of spherical polar orbitals and the formation of hybrid orbitals. The contribution of each spherical orbital into a hybrid orbital depends strongly on distance R from a nucleus to the dummy centre, and substantially alters when R varies. At two limiting cases R = 0 and R → ∞ spheroidal Sturmians are purely atomic orbitals, whereas at intermediate R they contain many features intrinsic to diatomic molecular orbitals. Applications of spheroidal Sturmian basis are discussed; Coulomb spheroidal Sturmians are asserted to be the most appropriate basis functions for diatomic molecular calculations. 相似文献
18.
19.
An exact solution to the problem of light scattering by multilayer axially symmetric particles is derived and some aspects of its computer-aided implementation are discussed. The main specific features of the solution are (i) separation of the incident, scattered, and internal fields into two parts and special selection of the scalar potentials for each of them; (ii) expansion of the potentials in terms of spherical wave functions; (iii) formulation of the problem in the form of surface integral equations; and (iv) solution of the reduced systems of the linear algebraic equations for the coefficients of the potential expansions. Mathematical justification of the solution is discussed, which is formulated in the recursive and nonrecursive form (for the T-matrix). The developed computer program has shown that the proposed approach makes it possible to consider axially symmetric particles with essentially different internal structures (i.e., with a spherical core, oblate spheroidal shell, or prolate spheroidal intermediate layer). The results of calculations of the optical properties of the multilayer nonspherical particles are presented and discussed. 相似文献