Symmetric euler-angle decomposition of the two- electron fixed-nucleus problem.
Optimum selection of Euler angles for expansion in eigenfunctions of angular momentum of two identical particles in fixed nucleus field
TWO-ELECTRON SYSTEM↗
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Partial wave theory of diatomic molecules. ii.
Wave function expansion of diatomic molecules in series of orbital angular momentum eigenfunctions
ORBITAL MOTION↗
The hyperfine splitting of the interaction energy of two hydrogen atoms.
Hyperfine splitting of spin interaction energy of two hydrogen atoms, determining eigenfunctions for effective Hamiltonian
HYPERFINE STRUCTURE↗
Controllability of distributed parameter systems
Eigenvalue-eigenfunction expansion methods for solving homogeneous boundary value problems applicable to control systems with distributed parameters
Herget, C. J.↗
A survey on some mathematical models of the very low frequency wave propagation
Mathematical models on very low frequency wave propagation, based on waveguide mode, zonal harmonics, eigenfunctions, and wave theory
Cheng, D. H. S.↗
Lower bounds to eigenvalues of the Schroedinger equation. I.
Optimum lower bounds to excited states of Hamiltonian having known set of eigenfunctions
Wilson, T. M.↗
Order of levels of symmetric Hamiltonians. I.
Bound levels of particle in symmetric potential, discussing ordering by symmetry types and eigenfunctions behavior for cubic and tetrahedral symmetry
Saffren, M. M.↗
Structure of the isotropic transport operators in three independent space variables
Based on the idea of separation of variables, a spectral theory for the three-dimensional, stationary, isotropic transport operator in a vector space of complex-valued Borel functions results in continuous sets of regular and generalized eigenfunctions.
Abu-Shumays, I. K.↗
Short-wavelength oscillations of cold-disk galactic models.
Cold disk galactic models free short wavelength oscillations, obtaining asymptotic approximations for eigenfrequencies and eigenfunctions of bending and planar modes
Hunter, C.↗
A note on the solution of Eddington's equation
Eddington equation for white dwarf pulsation solved by treating eigenfunctions as differential moment of inertia functions
Africk, S.↗
Modal decomposition of aperture fields in detection and estimation of incoherent objects
Aperture field modal decomposition of optical system in terms of integral equation eigenfunctions during detection and estimation of incoherent objects
Helstrom, C. W.↗
Transient solutions of the Fokker-Planck equation for a class of first-order phase- locked loops
Eigenfunction expansions of reduced nonGaussian phase error transition probability density function for first order tracking loop, analyzing spectral properties of Fokker-Planck equation
La Frieda, J. R.↗
The exact solution of the monoenergetic transport equation for critical cylinders
An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.
Westfall, R. M.↗
Adjoint variational methods in nonconservative stability problems.
A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.
Prasad, S. N.↗
The method of models in variational scattering calculations.
It is shown that difficulties in atomic scattering calculations that stem from the use of inexact target wave functions can be overcome by employing the so-called method of models, provided that the projectile is distinguishable from the atomic electrons. The proposed method of models consists in replacing the target hamiltonian by a model hamiltonian, of which the appropriate target state is an eigenfunction. A connection with the positron scattering work of Peterkop and Rabik (1971) has been established.
Drachman, R. J.↗
Resonance quasi-projection operators - Calculation of the super 2 S autoionization state of He/-/.
Development of a method to remedy the defects of the projection-operator technique for calculating electron resonances in scattering from many-electron targets. It is recommended that the projection operator Q be replaced by a quasi-projection operator which yields a discrete spectrum which can be made to be in essentially a unique correspondence with resonance energies. By relaxing the idempotency requirement, it is found possible to define two forms of this quasi-projection operator. The simpler of the two forms is tested on e-H and e-H(+) systems; the two lowest resonant energies differ by less than 0.01 eV from rigorous QHQ results. For many-electron targets it is further argued that replacement of the exact target eigenfunction by reasonable approximations in constructing the quasi-projection operator will affect neither the discreteness of the above-mentioned discrete spectrum nor the proximity of its eigenvalues to the resonant energies.
Temkin, A.↗
Asymptotic theory of a slender rotating beam with end masses.
The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.
Whitman, A. M.↗
Sound propagation in duct shear layers.
Consideration of the propagation of sound in a two-dimensional inviscid shear layer for given initial sound pressure profiles. The eigenvalue problem resulting from an assumption of separable solutions in a form first obtained by Pridmore-Brown (1958) is solved numerically. It is shown that although the resulting eigenfunctions cannot be proven to be orthogonal or complete, they can be combined by a least total error squared method to give a good representation of the initial pressure profile. The acoustic pressure in the duct is then easily calculated. The results verify all the predictions made in an earlier perturbation calculation. Moreover, they show that the refraction effect gets saturated at high subsonic Mach numbers and at high frequencies. The proposed technique may be used, if necessary, with impedance boundary conditions at the duct walls.
Shankar, P. N.↗