Article

Upper and lower bounds for the problem of a membrane with elastie support

May 1976
The Quarterly Journal of Mechanics and Applied Mathematics 29(2)

DOI:10.1093/qjmam/29.2.197

Authors:

Upper and lower bounds associated with the problem of a membrane with elastic support are derived from new hypercircle results and related extremum principles. Calculations are performed for a membrane in the form of a right-angled isosceles triangle and an accurate approximate solution is obtained.

Dual Extremum Principles and the Hypercircle for Some Ordinary Differential Equation Occurring in Plate Deflection Theory

Article

Jan 1979
J Appl Math Mech Z Angew Math Mech

R. C. DUGGAN

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Article

Unitary Approach to Quasielastic Scattering Reactions

February 2004 · Physics of Atomic Nuclei

The possibility of deriving an approximate unitary solution to integral Faddeev equations within the K-matrix formalism is considered. Explicit expressions for the amplitudes of elastic, inelastic, and quasielastic three-body scattering are obtained under the assumption of a mechanism of a truly single collision. Specific calculations are performed for quasielastic-scattering reactions of the ... [Show full abstract] d(N, 2N)N type. Good agreement between the results of these calculations and experimental data indicates that, in developing approximate methods, it is highly desirable to respect fundamental physical principles.

Chapter

CHAPTER 14. APPROXIMATIONS

December 1978

Mitchel Weissbluth

This chapter explains the derivation of the Schrödinger equation through a variational principle. The variational method achieves its greatest utility in the calculation of approximate solutions to the Schrödinger equation. It is supposed that ψ is an arbitrary trial function, which is intended to serve as an approximate solution to the Schrödinger equation. The chapter discusses the variation ... [Show full abstract] principle, according to which the best approximation to the eigenvalue is obtained by varying ψ or the parameters on which it may depend. A trial function that has been optimized with respect to the total energy is not necessarily the best function with which the properties other than the energy can be calculated. The secular equation and its solution provide a set of energies with the lowest one being an upper bound to the true ground state energy.

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Full-text available

On the Theory of Cascade Showers, I

February 1952 · Progress of Theoretical Physics

The improved mathematical treatment for the calculation of cascade theory is presented. The solution corresponding to a single incident electron derived by this method is identical with that of Snyder and Scott. The method is mainly due to the principle of analytic continuation but somewhat different from that of Bhabha-Chakrabarty. It is also applicable to other inhomogenuous ... [Show full abstract] integro-differential equations and in particular should be useful for further works on cascade theory. For an example, it is shown the lateral and angular distribution functions are derivable analytically by this method.

Last Updated: 22 Oct 2024